You can go here by train from Malmö, or from Copenhagen Airport. Flying to Stockholm (Skavsta) is another option, and driving down the E22. Kalmar does have an airport with connections to Stockholm Arlanda.
You can walk to all interesting locations. The city centre is relatively small, with two main squares. On one you find the cathedral (Domkyrkan) and the other is called Larmtorget. From the second you you can walk to the Baronen shopping centre. You an also rent canoes at the low cost hotel Svanen, and you can paddle your way around the centre, which is an island.