We are priced out of staying in London center . Our first time and have plans to explore the area where buckingham palace is, trafalgar sq, Westminster abbey. We found a reasonable hotel in Sutton but wondering if that’s too much out of the way . We want to have easy access to Heathrow via train / metro , we plan to have a day trip to Windsor castle or maybe hyclere castle , and of course we would like to spend a day exploring the tourist sights in the city center mentioned above . Should we try to get closer to the city or there train access from Sutton for all of the above?