I'd also recommend Wales. Abergavenny and the Black Mountains is lovely with cute little villages like Crickhowell and you also have the Brecons. It is very unspoilt, lots of nice pubs with good food. And you could go to Cardiff which is a great city, small but tons of things to do. As a Londoner myself I don't recommend it if you're on a budget. It is EXPENSIVE and you will just get frustrated if you can't afford to do things. You need a lot of inside info to survive London on a budget, from travelling on the tube (you need an Oyster card otherwise it's £3 for a single in the central zone), to getting cheaper theatre tickets. Ask away if you want!