The Airport Rostock-Laage  (RLG) lies near Rostock.
Ryanair has a service from Stockholm Skavsta airport (NYO) to Rostock-Laage (RLG) airport. Alternatively you can fly to Hamburg (HAM), Bremen (BRE) or Berlin Schönefeld (SXF) and travel by train to Rostock.
From Hamburg Central Station you can take the Regional-Express (RE) train to Rostock, or the faster IC (InterCity). If on a budget, buy a Mecklenburg-Vorpommern-Ticket. With this MV-Ticket, you can travel with up to 5 adults from Hamburg to Rostock. At weekends and during holiday seasons, you will see people (especially students) near the ticket machines asking whether you want to share a ticket, so it is worth arriving early and trying to find such an ad-hoc travel group. However, be aware that the "MV-Ticket", like all "Länder-Tickets", is NOT valid for the fast trains, IC or ICE! If you wish to travel via IC, you have to buy a ticket that explicitly states "IC".
From Leipzig and Berlin Central Station you can take the "normal trains" of Deutsche Bahn or the Interconnex, which is a lot cheaper - especially if you book online.
From Hamburg take the motorway A1 to Lübeck and from there the A20 to Rostock. It's a 1 1/2 hour trip. If starting in Berlin you take the A24 in the direction of Hamburg until the A19 crosses it. Follow the A19 towards Rostock. It's a trip of 2 1/2 hours. Beware of speed cameras especially on the A24!
Finnlines and Tallink-Silja run ferries from Helsinki to Rostock.
From the ferry terminal, you need to take buses to go to the center of Rostock. You can also head for the Rostock-North S-Bahn (train) station, about 1km away from the terminal. Note that you may get stuck at the ferry port on holidays when bus services are infrequent if you can't find the train station. A taxi ride downtown will cost you around 20€.
The port of Warnemünde, just north of Rostock, is used by cruise ships which dock at Hohe Düne. It can be reached easily by train (10 minutes) or taxi from central Rostock. All trains from Warnemünde stop in central Rostock, too. The train station is an easy three-minute walk north along the dock.
Hansa Rostock - The local professional soccer club.
KTV. The Kröpeliner-Tor-Vorstadt (KTV, "Kröpelin Gate Suburb") was the first part of Rostock built outside the medieval city walls, in the 2nd half of the 19th century. Originally designed to house workers flocking to the newly industrialised town, today's KTV is one of the most popular residential areas, especially with students and artists. It is here that you will find the highest density of bars, cafes and small shops selling handicraft or organic food. To get to KTV from Rostock's main shopping street (Kröpeliner Straße), follow it all the way to the west, passing Kröpelin Gate and crossing the tram lines. Everything in front of you now is already part of KTV. Check out the Doberaner Platz, where most tram lines stop, where the best Döner Kebab is sold, and where everyone seems to meet before a pub crawl with friends.edit
Stadtmauer (city walls), . While much of Rostock's fortifications were removed on the "sea"side (towards the river Warnow), a large part of the city wall remains on the "land" side and is certainly worth a visit. You will encounter 3 remaining gates, Kröpeliner Tor, Steintor (stone gate) and the oldest, Kuhtor (cow gate). Guided tours (some of them by a guide dressed up as a medieval night-watchman) are available and recommended for anyone interested in the history of the town. They can be booked under the stated link or in the tourist office. For the "night-watchman" tour, it is also possible to simply turn up at Petrikirche at 8pm if you're not with a large group, but the tour will then be in German only.edit
Climb the tower of Petrikirche (St. Petri's church), . open from 10am, closing time depends on the season (currently 4pm October to April and 6pm May - September - consult website if unsure). Petrikirche boasts the tallest tower of the three remaining churches within the old town. The church itself can be visited for free (open daily, mind the Sunday service 11-12am) although the parish will be grateful for any change you put in the collection pillar. For the tower, there is a small admission fee (3€; 2€ for students or with the Warnowpass; family ticket (2 grown-ups, 2 kids) 6€ plus 1,50€ for each additional child). Climbing the steep spiral stairs is fun and a good exercise! There is also a barrier-free option: The parish has had the original bell shaft replaced by a lift which brings you up to the platform. It offers good views over town, river and harbour. Many guided tours of Rostock also start in front of the church. Also worth keeping in mind: The parish has installed what is probably the only free public toilet in the old town (although, again, it might be a nice idea to put some coins into the collection column inside the church), also barrier-free and accessible from the outside, to the left of the main entrance.edit
Watch the sunset in the harbour. Take some drinks and food down and watch time pass by - as well as sailing boats, rowing boats, and plenty of seagulls. If it's herring season, the quay at the Silos will be full of fishermen. If you're not into bring-your-own, there is a number of restaurants and bars along the quay, from German, Italian and Greek to Spanish cuisine. Between the theatre and Latino bar "Besitos", you will find plenty of young people playing "Kubb", at least during summer. Why not try it out yourself? If you ask nicely, you are sure to be allowed a shot. Or buy your own wooden kit at the games store "Wupatki", Rungestraße 17. BTW: This part of the harbour is usually called "Strand" (beach) by locals, even if there is no sand within sight.edit
self-brewed beer at Trotzenburg, Tiergartenallee 6, . The Trotzenburg is brewing their own beer.edit
Exquisite, home-made chocolate and truffles at Schokoladerie de Prie, Warnowufer 59. You will also get freshly-ground coffee there, which is roasted at their place in Kühlungsborn. There, on the other hand, samples of the chocolate made here is also sold, so just visiting one of the two places gives you a chance to pick up both (much more variety of coffee beans in Kühlungsborn, though, and vice versa).
Café Lom, Barnstorfer Weg 19: studenty place with Indian-style food. Cheap and good.
Café Central, http://www.cafes-in-rostock.de/central/index.php In the middle of KTV, just round the corner of Doberaner Platz. Popular with students and other guests. Breakfast from 9 to 14; afterwards (and from about 11am), food is served until 22:30.
Likörfabrik, corner of Große Wasserstraße/Grubenstraße: nice little café, menu includes wraps as well as cakes. If you play the piano (read: play it well! It's students of the nearby HMT, the university of music and theatre, who are setting the standard), you can ask whether you may play for your drinks. Large groups may find it difficult to squeeze in when it's busy.
Marientreff, Bei der Marienkirche 1a: Enter the cute little courtyard just behind Marienkirche. In late spring/early summer, you can sit beneath a blooming lilac bush. Secret spot for home-made cakes and hot & cold drinks. Run entirely by volunteers of the Marienkirche parish and open daily, 11:30 - 17:30. From time to time there are also readings or small exhibitions here.
Plan B, Doberaner Str. 147. Its "Dinner in the Dark" events are popular.
Suppenwerk, Doberaner Str. 111. Soups! Good, satisfying, budget-friendly. Take-away also possible. Weekly menu. Opening times Mo - Fr: 11 - 16. http://suppenwerk-rostock.de/
Mambo No 1 http://www.pub-rostock.de/index.php/Kontakt.html Exactly why an Irish pub would be called "Mambo" remains a mystery, but the place is comfy and features regular live acts. Food: pub grub. Drinking guiness is fine but the cocktail menu deserves a closer look, too.
Jellyfish Hostel It is situated in a beautiful old Town House in the Old Town of Rostock just around the corner from the medieval Steintor. It offers beds in dormitories (drom 17€ in summer) and privates (from 23€ in summer). fee of 2,50€ for bed linen. Though the hostel is in the very city center - the Neuer Markt is two minutes by foot - it is really quiet there. It has a very nice common room, where breakfast (4€) is served as well, with two free internet PC's, a flatscreen, a stereo and a projector. In the fully equipped kitchen you can cook or just store your beverages in the fridge. The 8-bed dormitories are very spacious due two the very high ceilings, which even have stucco. The owners and all employees are quite young, easy going and very helpful.
Hanse Hostel - Doberaner Str. 96. Prices start at €14 for a bed in an 8 bed dormitory, for bed linen they charge €2 once per stay. Breakfast is available for €4, coffee, beer and soft drinks are available for €1. There is free internet, a great kitchen with a dishwasher, microwave, oven, stove and fridge. Bathroom facilities are very good. There is a TV, DVD and VCR downstairs as well as a bunch of board games, books and a dart board. The staff are very friendly and helpful and the place is clean, tidy and modern. Hanse Hostel is located at 96 Doberaner Straße near the corner of Lubeckerstraße, if your travelling by tram get off at the Maßmannstraße stop.
Jugendgästeschiff - According to the Tourist Information Office in Rostock this is the cheapest place in town with prices starting at €30 including breakfast, €20 if you have a discount card. Jugendgästeschiff is on a ship in the harbour basically at the end of Am Kabutzenhof.
InterCityHotel, Herweghstraße 51 (at the central train station)
Die kleine Sonne, Steinstraße 7, at Neuer Markt
Hotel Verdi, Wollenweberstr. 28 (near the University of Music and Theatre and the Petrikirche)
Rostock is a pretty safe town, especially in the centre and in Warnemünde. The sightly rougher suburbs of (Neu-)Dierkow, Lütten Klein and Lichtenhagen are not of interest to visitors anyway.
The most important safety advice might be to watch out for impudent seagulls that bear down with speed and accuracy in order to steal people's food on the Warmemünde promenade.