Anything within the inner ring should fit your needs. This is where you'll find the majority of sites that tourists visit Munich to see. The old city is rather compact, so unless you have mobility problems, you can get around on foot rather easily. The only area I would give a lower priority is the neighborhood immediately around the Hauptbahnhof. Despite hosting the city's best beer garden, this area is rather charmless and a bit seedy.
Within a few square blocks of Marienhof and Odeonsplatz is where you'll find lots of splendor and good restaurants, but expect to pay dearly for the privilege. Hotel Bayerischer Hof might be one of the finest hotels where I've stayed anywhere... but... not cheap at all. I've also stayed at Hotel an der Opera, which was nice enough, but a little costly for a hotel of it's quality. You pay more for the location than anything else.