Rick's guidebook has everything you need to plan your stay. There's really no need to rent a car. Munich's public transit system is very good. Have a look at getting day passes, good on buses, trams and subway.
Rick's book has good recommendations for smaller European style hotels, but we are staying at the Mercure Munich Altstadt. Yes, it's a chain hotel, but we've got points to use. :P You want a place within easy walking distance of an Sbahn or Ubahn stop. Staying in the old city is handy, but I'd avoid the seedier area immediately south and east of the Hbh.
Rick's City Walk will easily fill a day if you go at a relaxed pace. Then there's the Residenz and Nymphenberg palaces. Dachau is a half day - sobering, but completely worth your time. If you like Museums, there are plenty. The Pinakoteks (art museums), Egyptian museum, Deutches museum (science), city museum, just off the top of my head. There are several churches in the old city that are worth a look (covered in Rick's book).
If that's not enough to fill your time, you could do a day trip to Salzburg or to Neuchwanstein.