score:3
Optimal in terms of time or money?
London has 5 airports, but a US citizen will probably transit through Heathrow.
There are three reasonable options to go to central London.
Upvote:17
4 hours from Heathrow really isn't going to give you sufficient time:
You'd be left with 30-45 minutes of actual free time, and you'd be starting at Paddington Station, which doesn't give you much for an iconic photo.
And any complication (a delayed flight, a longer wait at immigration or security, a small train delay, etc...) would be enough to mess this up.
I personally enjoy madcap adventures doing layovers, and I'd skip this one. You could buy access to a lounge in your terminal if you want a more comfortable place to wait.