Which terminal/ airline/ destination?
Paddington is good for T2/3/5 (T4, less so) as long as you don’t mind paying for the Heathrow Express (you should be able to get an advance ticket at a discount). The downside is that you wake up in the morning and discover the trains are broken and you need an expensive cab.
It’s also reasonably easy from Wembley.
There are hotels attached to T5 and T4 if you’re flying from there, and a Hilton opening at T2/3 next year, but possibly not in time for you.
There’s also the convenient Hilton at
Hatton Cross tube station, which is only 1 or 2 stops from all terminals. First train just after 0500.
I wouldn’t stay at any of the hotels requiring a Hoppa or free TFL bus at that time of day.