Bavarian Geography

Nowadays Bavaria is divided into 5 main areas: Oberbayern, Niederbayern, Oberpfalz, Schwaben and Franken (which is again divided into Mittelfranken, Oberfranken and Unterfranken). You can see the capitals on the map.
The biggest river flowing through is the Donau, which goes all the way to the black sea. Other big rivers are the Isar, the Inn and the Lech, as well as the Main in Franken.

In the south are the big Alps (but only a small part of it belongs to Bavaria). In the north is the Fränkische Schweiz, which are not as high as the alps, but very lovely as well (with some amazing rock formations and old castle ruins).

As most tourists start their trip from Munich (as it has the biggest airport in Bavaria) we will take it as our starting point.
Going south from Munich (staying in Oberbayern or going to Schwaben) you will soon enter the Alpenvorland (before-the-alps-land), which is hilly with green pastures with cows and idyllic forests. Slowly the hills will turn to mountains and when you have reached the Alps, it isn't far to Austria anymore.
There are also a couple of big lakes south, where swiming as well as boat driving is alowed, and which are packed with people all year round. Small swimming lakes can you find everywhere. Over 10 around Munich, but those are of course not the least crowdiest...
Going east from Munich to Niederbayern the landscapes turn flat at first and then slightly hilly. Fields and small woods are the main picture here. Only in the northeast (after Deggendorf) the Bayrische Wald (bavarian forest) begins, which is not only a big forrest area, but also has mountains as high as 1400m!
North of Munich you will come through the Hopfen (??) area before the Fränkische Alp begins.
All areas of Bavaria are lovely and well worth a visit. It might depend on your interests where to go. Mountains or not is the basic question.