Cranfield is nice and busy. Maybe thats one you can consider.
Although it is stupidly expensive to land at, and the only thing to do is visit Cafe P - it's not one I'd put high on my list.
As mentioned, Duxford is fantastic - you can go round the museum, and there's bound to be something exotic flying.
Kemble is great (and has a good restaurant - AV8) although it might be a bit close for you.
Other good little airfields are Sleap, Tatenhill, and West Wales. This is all part of the fun of your new licence - enjoy it! (and congratulations - well done!)