top three picks right in city centre would be (in no particular order) Bayerischer Hof, Vier Jahreszeiten, Mandarin Oriental. truly stunning luxury hotels.
but there are a lot of very good hotels in the city, from the big names to private owned and the city is not that big that you could miss something out (if you don't pick the kempinski airport...). perfect public transport (safe) and most things in walkable distance.
enjoy!