Unfortunately, Miles & More redemptions are going to save you virtually nothing on economy flights within Europe. The cash element of an award flight is nearly always almost as much as just buying a cash ticket. The above example is fairly typical and is one of the reasons I ditched M&M. The program has its uses, but short-haul economy is definitely not one of them.

I would agree with other posters that, depending on your interests, Munich or Berlin is probably the best introduction to Germany. Köln (Cologne) would also be a solid choice.

Zürich is also a nice place to visit, but as already mentioned, will be significantly more expensive than anywhere in Germany.