I took a day trip to the Spreewald in 2015 and really enjoyed it. A very nice change from the big city. I'm not sure about April, though. You'll want a nice day. It's a fair walk from the train station in Lubbenau to the point from which the boats depart. (Maybe a mile? I haven't mapped it.) And the boats are small ones with no cover. Although people go there to walk or ride through the marshy area, the town of Lubbenau has some pretty architecture and will fill your "walkable town center" requirement.
I'd want to have some other options in my hip pocket for weather contingencies. Erfurt, Dresden and Schwerin can be reached by train in about 2 hours if you get the fastest early-morning train. They have handsome city centers, though Dresden's historic center was fire-bombed into nothingness during the war and only a fairly small area has been rebuilt in the old style.
Schwerin has a castle in a man-made lake with surrounding gardens, and it takes a good bit of time (indoors!) to see the castle. This part of Germany tends to be chilly and damp, though, so I think the odds of a nice day in April are not good.
Erfurt is a beautiful university town that came through the war in fine shape. It has a nice cathedral, but I think it's primarily a walk-around-outside place, so your enjoyment would be affected by bad weather.
Dresden has multiple world-class museums and is thus a good destination for days when the weather is grim. The Historic Green Vault requires a timed ticket; make that your initial stop and I think surely one ticket will be available very soon. It has an unbelievable collection of beautiful (and/or overdone) objects. The city's other museums (including the regular Green Vault) will more than fill the rest of a long day. The tourist office runs English language walking tours, but I don't know at what frequency in April.
