If money is a consideration -look at the Travelodge Feltham. It is a three minute walk to the public bus stop -buses run from 4am ish (it's used a lot by locals working at the airport so is very reliable) and with an Oyster card costs about £1 without it's £2.20. To get to Feltham the night before you catch a train from Waterloo -trains run late enough you could certainly enjoy theatre/dinner in the West End before travelling down.