Nothern way, 20 minutes gets you to ~Tufnell Park on the Northern line. You can also look around Seven Sisters on the victoria line, which should be roughly the same time. Brixton is about that distance from UCL on the Victoria line as well, but is in south London.
That's it in terms of distance, and hopefully that gives you some ideas for places to take.
Tube stations which serve UCL (comfortably) would be Euston, Euston Square, Warren Street, Goodge Street and Russell Square.