Berlin has post-WWII ambience and also a culture of youthful artists and designers. It’s a place to visit if you want both history and modernity.
If you go to Berlin, you can visit Checkpoint Charlie, the Berlin Wall Park, and other tourist attractions from WWII, and you can also go to lively clubs and explore hip boutique shops, small art galleries, and so on.
Berlin is also easy to reach from any city as it has an international airport, and is also a good destination if you’re touring Europe by EURail or are taking a bus connection.
I recommend spending at least a few days in Berlin, and bringing a light jacket because it can get a little chilly, even during summer. Finding a backpacker hostel or low-cost hotel in Berlin is not a problem as there are so many around, but book a few weeks to a month in advance during the high season, as they can tend to fill up quickly.
All opinions are my own.