There is a few direct buses from Växjö from the north. More often you have to change in Ronneby or take the train via Hässleholm. Timewise it's no big difference between them, but the train via Hässleholm requires to changes.
DFDS Seaways  provides a few places for passengers on their near daily service to Klaipeda in Lithuania, on board ro-ro freight ferries. The journey takes around 15 hours.
Its possible to fly in and out to Ronneby Airport and take a 20 min shuttle bus from there to Karlshamn. Ronneby Airport mostly connets to Stockholm, but also Visby (Gotland), Prag, Antalya and Palanga (Lithuania).
Sweden's best kept merchants yard from the eighteen hundreds, Skottsbergska gården. The basement is a two hundred grocery store on display.
The Cultural Centre, Vinkelgatan 8. Historic buildings of Swedish punsch factory, the silver forge, the art gallery, the print workshop and merchant houses converted into a museum. On the bottom floor and first floor is merchant lodges from the same time. Outside are stables, sheds and storehouses. Also just where they stood in the eighteen hundreds.
Östersjöfestivalen. Week 29 Karlshamn is sprung to life due to the big Östersjöfestivalen. The city is transformed to a bubbling entertainment city with music everywhere. It includes a lot of eating, drinking, rides, exhibitions, dancing etc... Also, a parade Thur and Fri evening.
More info at http://www.karlshamn.se/Ostersjofestivalen/ (choose "Välj språk" up in the right corner to change language (with Google translate))
Karlshamns flaggpunsch . Sweden's most famous punch. This traditional liqueur can be bought in all Systembolag all over Sweden, and it is nowadays made in Åbo, Finland. However, the name strongly associate it to Karlshamn.
More information about punsch at Karlshamns museum  och Wikipedia 
Brygghus 19 . A locally brewed beer. Can be found in a few local restaurants (no pubs yet) and at Systembolaget.
Sushi Bar Maki, Kungsgatan 22, 374 35 Karlshamn, Sweden, ☎ +46 454 159 44, . 11.30-20.00 M-F. Great little sushi place in the centre of Karlshamn run by a cool Swedish-Asian couple. Relaxed vibe, great fresh food, good prices. The man takes the orders and tells the jokes while the woman serves up the freshest maki, nigiri and sashimi in Blekinge. There's also some great mixed plates: including crowd favourites Nintendo (8 pieces) and Super Nintendo (16 pieces).65-180 SEK. edit
Trail of the emigrants, Follow the road from Eriksmåla in Småland to Karlshamn that the emigrants took in the emigrants book series, by the famous Swedish novelist Vilhem Moberg. A trail tens of thousands of people traveled on, fully or partly, on their way to Karlshamn to board a ship to America. It's 50 km and littered with historic sites along the way (and sometimes far out of the way), to teach you how life was a hundred years ago. Tourists offices have a brochure with a map and description of the sites.
Ire, 100 ha. A nature reserve 20 km north of Karlshamn. Efforts has been made to have it keep its look from when it was a farm, since modern farming techniques has never been used here. It is used for educational purpused by the local Government to teach pupils how farms used to look like, how people have lived of nature and how it changed the landscape. To get here, follow road 29 north and signs will point in the right direction.
Loberget, 124 ha. Just north of, and similar to, Ire (mentioned above).
Långasjönäs, 533 ha. A nature reserve with a lot of walking and skiing track. On the south tip is has a camping and cottage area and beach. It's also possible to fish game fish in the lakes.
Eriksberg, 790 ha. A game pasture with red deer, fallow deer, moufflon sheep, wild boar and European bison. During the summer you can drive around in your own car. During the rest of the year it's only open for guided tours.
Tjärö, 76 ha (the entire island including surounding islets). An island with meadows, grazing animals, stone fences and walking tracks. Price for a return journey boat from Karlshamn: Adult: 100 SEK, Children 3-12 yr: 50 SEK.
Tärnö, 30 ha. The island furthest out in the archipelago. On a beautiful day, from the top of the mountain Drakberget (Dragon Mountain), it's possible to see half of the Blekinge coastline. It's possible to rent a boathouse through the tourist information. It is reached by boats that depart from Karlshamn and Matvik.
Tararps gigant pots Big round holes in the mountains, some as big as four meter in diameter. Created when the ice sheet melted. Stone and gravel swirled into the moutain. For pictures and map, see this page: 
Nature reserves that are less accessible and harder to walk through
Grimsmåla, 11 ha. 3 km south of Ire (mentioned above). Contains gravel formations in the form of boulder-ridges.
Hoka, 3 ha. 7 km south of Ire (mentioned above).