Stan. I've been to all three (Prague, Berlin and both Buda and Pest (both sides of the river) as well as Istanbul (again, both sides).
Go. Please go.
Take one of the many river cruises, or just go there, find a guest house and hang out. Don't forget to stop by Salzburg, too - you won't regret it, any time of the year (but Christmas is extra-special). If you can get to Istanbul, THAT would be wicked-awesome, too! (But I'd personally go to Salzburg first). There is so much history over there from so many early cultures that you feel like a sponge, just soaking it all up and when you return home you're dismayed at how much has leaked out of your head.
Have breakfast at a small cafe and meet locals. They will be thrilled to speak with you and learn about you and share their cities with you. Ask them for cool things to do. Become a part of their culture (I know....You've already done this).
I was once in Prague for a business conference/meetings and ended up "being delayed" at the end of the conference and "had" to spend a weekend there. I was escorted about the city by a potential customer and thoroughly enjoyed the visit as we found out-of-the-way places and even some relatives.
I would go back in a heartbeat.