If we're talking central London, I'm partial to Bloomsbury. It's very centrally located and is, generally speaking, a relatively quiet area. The British Museum is nearby, as is the Russell Square tube stop. I have no idea what rentals are available though. I have no idea what cycling in the area would be like. I'm not sure how inclined I'd be to ride on the streets in Central London. I think taking a day trip to, say, Oxford for a bike ride would be more fun.