Wouldn't recommend White Waltham without a car unless you don't mind expense. It's costly to keep getting cabs from Maidenhead, I've tried it! Expensive club, too, if you're trying to keep it cheap.
Elstree is quick if you put a bike on the train - the train service is good and also cheap. I think Denham is as well. Stapleford, I don't know, but it might be a bit further; you'd probably need to get a cab. Redhill is very close to Nutfield Station (walkable, even), but the train service is quite infrequent.
Biggin Hill is a train journey from London Bridge to either Orpington and then a R2 bus or to Bromley South and a 320 or 246 bus. Probably the quickest I've found, especially if you're SE based, but more expensive. Might be worth a look though - I think Alouette are quite cheap.