Your "First week of April 2015" is pretty specific.
You mentioned Bavaria, so probably flying into Munich. We did this last April. There are many good choices. We like trains; but everyone has to be able to carry their own luggage. Try to be reasonable in what you take for a week. Public transport:
http://reiseauskunft.bahn.de/bin/query.exe/en
Our first stop was in Landshut, bus & train from the airport. A beautiful little town on the Isar River. It has many colorful building facades and its own castle. We had excellent weather. Try the Hofbräuhaus (not like Munich's) or Augustiner at St. Martin's church for very good German food. We stayed at the Cafe Himmel and liked it. Our pictures from April:
http://mcchelsea.smugmug.com/Other-2/April-2014-Landshut/38726799_vsK4kd
A short train ride from Landshut is Regensburg, a Unesco World Heritage Site for its Middle Ages buildings. Wonderful walk around town. I really liked the Kunstforum Ostdeutsche Galerie Regensburg, which is a small, somewhat quirky art museum. Regensburg has a several great churches including an 1141 A.D. cathedral. It also has Roman ruins. Good to read its history (~Wikipedia) before you go. We like the Weidenhof Hotel about 4 blocks from the train station and are staying there again this coming April.
From Regensburg you might visit one of several places: Bamberg, Nürnberg or the Rothenburg. Rothenburg is an infamous tourist haunt but beautiful and fairly quiet in April. It is a great place to take pictures. A bargain stop is the Hotel Raidel. Gasthof Greifen is very picturesque. Bamberg is another favorite of ours. Hotel on Dom was very nice. Nürnberg is a beautiful old town but April is trade fair season and rooms are hard to find except on weekends.
We usually finish our trips in Freising, which is closer to the Munich airport than the city itself. We like the Hotel Bayerischer Hof or Hotel zur Gred. Visit the Domberg (cathedral on the hill) where the prior pope was ordained. Freising claims the oldest operating brewery in the world: Weihenstephaner. It is also a school of brewing. There are shuttle buses every 20 minutes to the airport for about 4 euros per person. You can also catch a taxi for about 30 euros. Our rainy April pictures from 2006
http://mcchelsea.smugmug.com/Travel/Freising-April-06/1402301_pTGGtq
These are all walkable towns of various sizes. I have left out much more than I l have mentioned. We have visited 3 times in April with mixed weather but enjoyed every trip. Not too expensive umbrellas are available there if you happen to have rain.
We made all our reservations through Hotel Reservation Service: HRS.Com