Stay Munich is an apartment hotel. it's about €990 a month - that might be a company rate though. Facilities include: gym, one free shared internet terminal, sauna, weekly cleaning. Ottobrunnerstrasse - to get there, get the S-Bahn S5 from Ostbahnhof and get off at Weddingerstr. or Woferlstr and walk up from there.
Note, they don't accept pets.
See also: