With an 8am departure, unless you're intending to pay for an Uber/taxi/car service you'll want to be in an airport hotel - the tube service in the morning would just about start early enough but would be an uncomfortable rush, and there's really nothing around Paddington that would represent a significant gain in terms of location over LHR if you were considering the Heathrow Express/Connect as possible options. Central London hotels are also expensive, so you'd be paying twice as much for only a handful of hours in the room.

Making the assumption that you're going to be flying on a Star airline as a UA 1K, the best bet would be something on the Bath Road, or alternatively the Hilton Garden Inn. The HGI is very close to Hatton Cross tube from where it's about 40-45 minutes into the West End, and there's a frequent bus into LHR (#285 to the Central Bus Station) the following morning which is free and only takes about 10 minutes.