Here is a listing of hotels in Munich that I compiled from recommendations on the board.
Blauer Bock
Viktualienmarkt
Royal
Uhland
Seibel
Münchner Kindl
Of these properties, I have only seen Uhland from the outside. It looked nice and was in a nice neighborhood. Depending on the date, it might not be in your price range, but worth checking.
Note: I have never stayed at any of these as, when I stay in Munich, I almost always (16 nts) stay at a non-English speaking hotel in the suburbs (EZ $72, 2BZ $98, Ü/F).
For staying near FRA, I have stayed at and can recommend Hotel Königshof in Mainz. It's just across the Bahnhofsplatz from the Hauptbahnhof, 2 S-Bahn/hr, about ½ hr.
As for Frankfurt Hbf to FRA, there are four S-Bahn per hour from the underground (tief) S-Bahn station at Frankfurt Hbf to the airport. These are S8/9, direction Wiesbaden or Mainz. So if you go down to the underground station, you can count on an S-Bahn within 15 minutes.
There are also some S-Bahn and regional trains leaving from assorted tracks in the ground level part of the Hbf. Check the schedule before deciding which part of the station to go to.