The common advice is, that an investor should concentrate on well-known cities and here on the areas which are most wanted for renting.
If you have a good consultant nevertheless it might be worth to look also for the "Speckgürtel" of some major cities, like for example the north of Hamburg (and south of the Elbe River) or the areas west of the Ruhr-Gebiet. These areas have a remarkable good infrastructure combined with much lower prices, you would find in the central areas.
There are also some "inner peripheries", which can be discovered and developed.
The places with the highest rental level are: Frankfurt, Munich, Stuttgart, Duesseldorf, Hamburg, Koeln. In Berlin the risks are higher than other major cities. The differences within in Berlin can be enormous - concerning the prices as well as the chances.
Leipzig and Dresden can be interesting, but you need a very careful research and good advice. Other towns in the former GDR can have chances, but need extremely carefully checking also.
In the early nineties real estate investments in East Germany were intensely supported by tax advantages. Now many flats in eastern Germany are empty – and not rentable for yet a while. The number of inhabitants decreases in many areas.
As everywhere there are exceptions and there are some areas (f.e. in some small towns at the Baltic Sea) where the demand is still higher than the offers.

Within some cities in eastern Germany you may find also elderly people from West Germany looking for cheap homes. These are special markets.

Cities in the western part of Germany like Frankfurt, Hamburg, Munich and Stuttgart have been and are rather stable in rent. The rents partly increase, especially in the very good city areas. Because the number of new houses built per year had been decreasing over the past fifteen years a general rise of prices in those areas can be expected - and has started already.
Refurbishing of old buildings might be very sensible in many cities. But: to organize such a refurbishment can be very complicated, if you don't find a way, which is agreed by the tenants, living there.
The legal rights for tenants are rather strong.