Are you saying you have 2000 Euros a month to spend on housing? I don't think you'll have a problem with the cost if that's your budget, unless you want a mansion. There are many topics about housing on this website. Rather than point you to a specific one, I'll encourage you to have a look around and see what they say. The search box at the top will help you. Areas close to the city center include Maxvorstadt, Schwabing,
Lehel, parts of Sendling, Glockenbachviertel and parts of
Neuhausen. Looking in the Munich - "accommodation offered" section of Toytown isn't a bad place to start a specific search for a place to rent.