There are many threads in the Germany forum that detail dozens if not hundreds of charming German towns all over the country. Visiting some of those along with a few of the major cities/historical sights would make for a great trip. The German rail service is very good, and there are great deals on regional train tickets.
Plan as much time as you can in Europe, because you'll be very sorry about having to miss a lot of great places if you have made the trip shorter than it needs to be. There are wonderful places to see in neighboring countries as well as in Germany, but there's a lot of variety within Germany alone in terms of both scenery and towns/cities.
Recognize that the day you arrive in Germany you may well be severely sleep-deprived and jetlagged, so that's a day to plan to do things like walking around outdoors, not heavy-duty sightseeing. It's also fine to hop right on a train to get to your first stop.
Depending on what places you want to visit in Germany, it may make sense to fly into and out of different cities. That is a "multi-city" trip when you're looking at the flight websites like Google Flights. Fares will vary by date and your German gateways. You can probably get an idea by checking now from your origin to "Germany" on GoogleFlights. See what cities are cheapest and which are more expensive. For me, Frankfurt and Munich are usually cheaper than Berlin, but it might be different for you.