We finally decided we would stay out at Heathrow so we are near our departure spot, plus right beside a Subway station so we could head to downtown London over the course of the next 3 days.
This is a copy of the subway map. Click the map and you go to the real interactive map site
Mind you our trips will be very simple as we simply walk from our hotel to the last stop at Heathrow Terminal 5 and head to various stops downtown London. Mind you we have to transfer but should be fairly simple.
Over the next few days we can see the sights and sounds of London taking in such things as
Tower of London
London Bridge
Borough Market
Big Ben at Parliament
The London Eye
Picadilly Circus