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.
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).
Frequent buses connects to everything outside the city centre. Everything in the city centre is within walking distance, or a quick bike ride.
A couple of boats traffic the archipelago. Mostly or only during the summer, depending on the route. Routes and timetables can be found at Visit Karlshamn .
Axel Olsson's statue of Karl-Oskar and Kristina.
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.
Kreativum Science Centre , Strömmavägen 28.
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))
Hostel Karlshamn , Surbrunnsvägen 1C, tel. +46 454 14040. Double 420 SEK.