Good morning from Pekin, Illinois: we are going to London to see our new grandson at the end of May

Good morning from Pekin, Illinois: we are going to London to see our new grandson at the end of May and wish to find a Heathrow Hotel the night before we leave, as our American Airlines flight leaves wachusett village inn at 7 am. Does anyone know for sure that AA flies out of Terminal 3? What hotels would provide easy access to this Terminal? Any suggestions would be so appreciated. Thank you. Melissa
We will be staying at the Renaissance London Heathrow, for the same kind of reason, though in reverse, we will not get to the UK until noon having flown all night (like you out of O Hare) and as I had a certificate for a free Marriott night chose this venue to get a nap, an early dinner and wake refreshed the next morning for our car rental and drive to the Cotswolds. The nightly rate was quite reasonable, go to the main Marriott website and put in London, U.K. for your search and dates and the Renaissance will show up there, plus you can key in AAA, senior rate or Government for discounts and specials. I called the hotel and find there is a hopper bus from terminal 3 (if you take the tube out there) which is about L5 pp, or a Taxi which you'll probably need that early in the morning about L15. It's a 10 min drive from Heathrow wachusett village inn and yes you usually come in and depart from Terminal 3 with AA. The Brits want you at the airport 3 hours before flight time for International flights wachusett village inn so you'll need to be there about 4 a.m.
Unless the Heathrow Airport website is lying then all AA flights are from T3. Therefore you could use any of the Bath Road hotels and use the Hotel Hoppa or - better still - FREE buses to get to / from the Central Bus Station which is a short walk from T3.
We used Hoppa Bus once and it was late (and we already cut it close for our flights). So we twice took a taxi, about 15 GBP I believe from this Marriott to T3. I think the Hoppa is about 4 GBP each (haven't checked in 2 years) so a taxi wasn't much more for two people. ANd yes, AA does fly out of T3.