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))
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.
Hostel Karlshamn , Surbrunnsvägen 1C, tel. +46 454 14040. Double 420 SEK.
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.
Nature reserves that are less accessible and harder to walk through