I've booked a hotel in Kalmar: Hotell Hilda.

Here's what Rough Guides says about Kalmar:
Delightful, breezy Kalmar, set on a huddle of islands at the southeastern edge of the county of Småland, has treasures enough to make it one of southern Sweden's most delightful towns – a fact sadly missed by most visitors, who have their sights set on the Baltic island of Öland, to which Kalmar is joined by a six-kilometre bridge. Surrounded by fragments of fortified walls, the seventeenth-century town centre, set on the Kvarnholmen islet and connected to the mainland by several bridges, is a mass of cobbled streets and lively squares, lined with some lovely old buildings. Close by is the exquisite castle, Kalmar Slott, scene of the Kalmar Union, which brought Sweden, Norway and Denmark together as a single kingdom in 1397, and now one of Scandinavia's most finely preserved Renaissance palaces. Just a short walk in the other direction, there's the fascinating exhibition on the Kronan, one of the world's biggest warships, which sunk off Öland over three hundred years ago. Even now, new finds are being discovered, helping to piece together the world's most complete picture of seventeenth-century maritime life.
Here's a picture of Kalmar Cathedral:

And here's the castle:

Whether I get to take an excursion to Öland or not, I think it will be well worth the two nights stay I have planned, though I won't arrive until late afternoon or evening, depending on my train connection.  I'll be coming from Ærø, which means a 1 1/4 hour ferry ride followed by a 6 hour train ride including 3 connections.  From Kalmar I'll travel to Stockholm, about 4 1/2 to 5 hours on the train, so I could easily spend a good portion of that day in Kalmar or on Öland before catching my train.