A friend and I are doing a walking tour in the Lake District, the Cumbria Way, in early September. We'll have three days at the end of the tour to do some additional sightseeing, which may include a day at Hadrian's Wall near Carlisle, the ending point of our walking tour. We've thought of going on to York, but it seems too far from London to travel back to Heathrow for our midday departure on Sept. 15 (Sunday, trains may not be as frequent). I'd love suggestions for a destination that's within two hours of Heathrow.
I would suggest Windsor. Lots of good hotels, B&B's. You could have a look at Windsor Castle and then walk around town. Cross the bridge and walk over and take a look at Eton. Easy transportation to Heathrow from here.
2 hours away from London by train on a Sunday with a noon departure is unlikely to get you to the airport on time. If it is a noonish departure to the USA you need to be at the airport 3 hours ahead. That's 9am. An hour from the main stations in London by Underground means being on the Tube by 8am. Many mainline train routes into London don't start arriving into London much before 9am on Sundays. That's if there are no weekend engineering works on either the trains or Tube. Both are relatively common on weekends, especially Sundays. I would suggest staying the last night either in or near London, and double checking your Sunday morning travel arrangements.