I'd recommend Berlin, we'll certainly go back there, it's a great combination of history, architecture (Sir Norman Foster's glass dome on the Reichstag is well worth going to the top of
http://www.galinsky.com/buildings/reichstag/ cafe society, great restaurants and shopping (on the K'Dam). Also, depending on what you're into you've got the New National Gallery and the Bauhaus Archive.
It's also cheap to get there and to eat and drink!
I agree with you about Budapest, really enjoyed visiting but would probably not rush back. Paris is always a joy to visit, love it. Prague I enjoyed and am going back in November, but only as my other half couldn't make the first trip there. New York is great but you do need longer than a weekend there.
How about the new Ryanair routes to places like Riga in Latvia and Oslo(depends on where in the UK you're flying from of course).
Happy planning