I second the Hilton Garden Inn T2&3. SO convenient.
I have also stayed at the Hilton Garden Inn London Heathrow Airport Hatton Cross.
It’s much cheaper. However, you have to make your way to the Underground station and take the Piccadilly Line to Hatton Cross. I think it’s a free ride.
The hard part is dragging your luggage up two flights of stairs to get out of the Tube Station. Then it’s a 10 minute walk.
I finally decided to spend the money and stay right at the airport. Decent restaurant downstairs and a cool bar that serves food at the top with views of the runway. You can also get sandwiches/salads from M&S or Boots at the airport to eat in the room.
Quick walk through the Parking Lot after you exit the Arrivals area at T2.
I am staying 2 nights as well, going into London for the day - Tube takes about an hour depending where you want to go.