US citizens do not require visas to enter the UK, other EU countries, and some other countries. To leave the airport at Heathrow you will need to go through customs and immigration, and then go back through again on your way out, so you have to allow time for that. Heathrow is a bit far out, but it is doable to go into town for a longish layover.
If I were you I would take the tube to the centre of the centre, Charing Cross, and pop in to the National Gallery (entry fee, thanks to socialism, GBP 0.00), right on Trafalgar Square, throw in a lunch at one of the nearby pubs, and then pop out to Heathrow again on the Tube. That way you get the flavor of the place but avoid the stress of trying to do too much in a short time.
(Amsterdam, as mentioned, is fabulous to visit for a layover, as long as you don't get too ... *confused* ... to find your way back to the airport.)