seeing as i pass through heathrow daily on my way to and from school, there are many many hotels at least such as holiday inn and travelodge which are opposite the airport but there might also be one (might being operative word) in harmondsworth which is in the heathrow area. Also, there are some on the Bath Road in hounslow but they don't look very good. Regarding getting to the airport, all the hotels have a national express bus which goes to the terminals (charge applies) and many are on the bus routes, U3 from harmondsworth, 222, 81 or H98 (be careful where you get off) go to the bath road and then either the 111 or 140 into the airport bus station. These two can be used from places on the bath road in the heathrow section of the bath road along with some other buses (worth looking up). If you find a place you can go to TFL Journey Planner and research times and routes.
Please don't book the Renaissance on Bath Road. We stayed there twice - the first time was fine, but then the hotel was taken over by new management. It's a long story but the second room we ended up with was absolutely filthy and we were so jetlagged that we couldn't be bothered to complain a second time (the first room was located in a corridor having electrical works being carried out ie drilling, and we were put there after having said to the desk staff that we were desperate for some sleep). The second room's bathroom had a broken loo seat that almost injured DH (not saying where!) and blood down the shower curtain. It was absolutely disgusting but I couldn't muster the energy to do anything about it - won't let that sort of thing happen again though!! I got my own back by doing a review on TripAdviser, and wasn't the only one to have those problems. We've booked the Holiday Inn off the M4 for the night b4 our holiday in June - I'm hoping it's OK!!
We're flying from Heathrow in August and we're wondering whether it's worth staying up there the night before. As far as I can make out, all the hotels are a shuttle bus away. Check out this map from Trip Advisor, Mrs Potts.