I would recommend Prien am Chiemsee. The cheapest hotel I found was EUR 39,- per night per person for double room (20 minute walk from the lake Chiemsee.
There is a huge lake where you can take a ship to the Herrenchiemsee island to see the last of King Ludwig II's castles (there are also museums and cafes) and to the Fraueninsel island (which is small and you can walk the whole circumference in about 15 minutes). On the Fraueninsel you can visit the church and shop of the Monastery (which sells great liqueurs which the nuns make themselves!!!)
You can hire a speed boat/pedal boat/rowing/sailing boat. The best speed boat that we hired was not sooo fast but had sonar which detects the depth of the water - which is useful for detecting rocks or shallow water which can damage the boats, or if you are not so confident in deep water, you know how deep it is before you jump. It also told you the temperature of the water (which is also a good idea sometimes before jumping in

When in shallow water, the engine automatically slowed down until you got into deeper water. You also get a built-in radio/cassette player. This particular boat was a bit of a pig to climb back into from the water as it had no ladder!!) Would be great with a crate of beer and food.
There are also a number of restaurants where you can eat freshly grilled fish from the Chiemsee lake, which is really tasty!! We ate fish every day!

There are also a number of other activities that you can do in the area, including shooting, horse riding, hot air ballooning. The alps are also very near, so probably very nice views and walks.
The ship to both islands and back costs about EUR 11,-.
The entrance for the Herrenchiemsee Castle is about EUR 7,- and includes both museums (if you do not have time to see everything, the tickets are valid for up to 6 months for the things you did not manage to see

Speed boat hire is about EUR 7,- to 10,- per 1/2 hour and seat 4 to 7 people depending on the boat.
To get to Prien, you can use a Bayern Ticket (which is EUR 25,- for 2 to 5 people one-way) and takes one hour or so on the train, so easy to go on a Friday night or Saturday morning and then stay until Sunday.
Well recommended! We are gonna go more often!!
For more details on where we stayed etc please feel free to PM me.