I sometimes think that I have taken every London walk that there is (I lived in London for a while and visit there about once a year). I think that they are almost always very good, but they have gotten crowded over the years. If you see a walk led by Emily, take it. She is fantastic ... an RSC actress who always gives a very fun tour. The pub walks in the evening are also very enjoyable.
Regarding Heathrow hotels, how late will you arrive or how early will you leave to go back to the U.S.? My question is do you need to stay at Heathrow? If not, another option would be to take the tube from Heathrow to Earls Court or Gloucester Road. Both of these stations are on the Picadilly Line and are about 45 minutes from Heathrow. There are a fair number of reasonably priced (for London) hotels within close walking distance of these stations. Unless I had a very early morning flight out of Heathrow, I would probably choose to stay in London.