We have one evening in London on a layover..flying into heathrow..need not too pricey hotel within walking distance of some cool London sights
I like the Premier Inn at County Hall. It's right next to the London Eye and Big Ben is just across the bridge. Reservations can only be made at this site:
http://www.premierinn.com
Agree with the Premier Inn County Hall, around 100 GBP.
You can save yourself about 20 GBP ($US40) by staying at the Premier Inn Kensington. This is ultra convenient for Heathrow. The London Underground runs from Heathrow to Earls Court direct every 5 minutes and costs just 3 GBP for the 40 minute journey.
I would just suggest that since your time in London is at a premium, I would recommend taking the Heathrow Express, which gets you from Heathrow in to Paddington Station VERY quickly. It's definitely worth the extra cost over taking the tube.
Try Orbitz for a hotel by the airport. I've gotten great rooms for as little as $79. (You do have to pay for the airport/hotel shuttle o/a 3GBP, maybe 4). Take the tube into town (from Heathrow) and see what you can see. Tube back out (about 30 min.) Ask at Heathrow about late night schedules, frequency ect.