Munich or villages around Munich?

The only obvious difference between city centre and suburbs or even further out are rental costs and commuting times.
International schools (with English instruction) only exist in or near the city, but in my opinion a public (German) school is anyway better for the kid.
There is no school ranking, because quality differences are negligible (purposely kept small by policies, to give all kids the same chances). You could visit a few schools near your chosen residence and talk to the teachers to get an impression.
Some schools offer integration classes ("Förderklasse") to get foreign kids up to standard in German and other subjects before joining regular ones. But at only six years old and entering the first year of primary school, this is not necessary and they normally put all kids together - that way the non-German ones learn at record speed and have no obvious disadvantages later.
Alternatively, you could put her in kindergarten for another year and start primary school at seven years old.