Dnipropetrovsk is an industrial centre of Ukraine that was a hub for the Soviet military industry. As such, no foreigners were allowed to visit without official permission until the 1990s. As an industrial centre still, it suffers from heavy pollution issues, but is generally well maintained and provides an interesting insight into real working life in Ukraine.
Be aware that while Dnipropetrovsk is located in Ukraine, like many cities of Eastern Ukraine, it is very rare to hear people speaking the Ukrainian language.
Dnipropetrovsk International Airport (IATA: DNK) is served by both Ukrainian and international airlines. It is located about 15km outside of the city center. It can be reached by taking marshrutka #60 from the train station or #109 from Chkalova street.
If you're in a hurry, it is best to take a taxi. A taxi to the airport from the city center will cost about 100UAH. Foreigners should be ready to pay up to 150UAH.
Recent merger of almost all independent Ukrainian airlines into UIA (Ukrainian International Airlines) has bumped airfares up considerably. Flights to/from Kiev run about USD 110 each way (January 2013).
Train is the recommended means of transportation and the city is well connected to all Ukrainian cities, as well as other places in neighboring countries.
Since Euro 2012, a brand new high-speed train has become available for an easy 5-hour trip to/from Kiev (there is even slow wifi!). The train is called "Interciti" with daily departures from Dnipropetrovsk at 07:30 and 17:30. Be sure to check the latest official timetable as schedules frequently change. 
It is better to choose another means of transport. Ukrainian highway police are extremely corrupt and will not hesitate to confiscate your passport until you have provided them with a sufficient bribe.
Roads in the Dnipropetrovsk region are in very poor shape. If you decide to take a bus, you can be sure you'll have a bumpy ride. Check the bus station site for a timetable of departures. 
Usually it is better to just go to the bus station, which is located a few minutes walk from the train station, and ask for the next departure to your desired destination. There will be plenty of drivers and possibly passengers willing to sell you tickets.
There are reports about ferries that go down the Dineper from Kiev.
There are frequent Marshrutkas, trolleybuses, and trams which run to all parts of the city. Trams and trolleybuses cost 1.5 UAH. Marshutkas cost 5.0 - 9 UAH.
Marshrutkas run on a loose schedule and need to be flagged down. Similar to public transportation elsewhere in the former Soviet Union, people usually pack themselves into a mini-bus like canned sardines. Expect to need to push your way through to the door when exiting or simply shout "prai-tI mOzhna?!"
It is common for men to give up their seats for women and the elderly. If you refuse to do this, old women will stand near you and press their stomachs or purses into your face until you stand up.
Take a walk in the new European square and visit the beautifully painted town cathedral before taking a walk down the main boulevard to the military museum and the monument with a beautiful view over the Dnieper river. There is also Historical Museum, Diorama “Battle for the Dnieper River (Second World War)”, Shevchenko Park, and Potemkin Palace nearby.
If you get time it's worth visiting the island parks on the Dnieper. Walk up the main boulevard for 5 blocks from European Square and then turn left. Continue down to Shevchenko park where you'll find a bridge that takes you across to one of the island parks. Here you can enjoy some relatively clean air, take a quiet stroll in the center of the city, pick up an ice cream or beer, and take a ride on some of the features of the old Soviet-style funfair.
There is no shortage of Teacher positions for native English speakers.
Borscht, cutlet po Kiev, and cutlet po domashanoy, olivea (mayonnaise salad) and plove for a good rice dish.
For a quick meal get a schwarma, there is a great place in the city center.
Though there are few quality drinking spots some do exist. The best would be Reporter on Karl Marx - a couple blocks past the town square. The second would be Master Schmidt, which has some live music and is a bit more alternative (on Schmidt Street about 3 or 4 blocks up from Karl Marx). For more of a club scene there is Labyrinth and Berlin (inquire locally for the exact location). And, if you choose to be really adventurous you can attempt a Metro Party - getting off at each of the 5 metro stops and drinking a drink. Lastly, for more of a local scene you can simply have a drink on the street-- by the river which is a quite nice walk, or just in the city center. This is the custom known as drinking "na lavochke."
There are a nice amount of hotels around the city. It's also possible to rent an apartment.
Mini Hotel Vesna - Minina Street 9, Dnipropetrovsk, 49000, Ukraine Booking.com's blurb: "Centrally located in Dnepropetrovsk’s business district, Mini Hotel Vesna offers rooms with a balcony. It also features a bar and 24-hour front desk. Free Wi-Fi is available in all areas. Rooms include a seating area with a TV and refrigerator. Each private bathroom is equipped with a bath." Prices: 250-400 UAH per room.
Hotel Dnipropetrovsk. Along the embankment and close to the city center, address 33 Nabereznaya. Rooms "economy-class" on the 6th floor in "1970 years like style" and all furniture not maintained, looks very old and ugly.
Be wary of groups of drunken people roaming around. Be careful drinking on the street at night because although the number has decreased since the 1990s, Gopniks (robbers) still exist in Dnipropetrovsk. They are people that enjoy drinking and fighting and little else and will not hesitate to fight you.
Be aware to visit quarters, such as Topol', Klochko, Livoberezhnuyi. There are so many robbers, so care about yourself