If you're thinking of something a bit quieter, it might be worth looking at Richmond. Really nice area and only 30 minutes to central London on the District Line. Overground trains also available from there.
There is a Premier Inn there and it's within easy walking distance of the station and high street, although a bit further away from the top end of Richmond, which is right on the river and has some excellent walks. Might be worth having a look at the Richmond Hill Hotel - I haven't stayed there, but have been to a couple of functions there and it seems good. Not sure price-wise, it's posher than a Premier Inn but then it's not central London which should help.
Richmond has a great vibe - the high street is cool, lots of great coffee shops etc.