There isn't one particular one, any of the hotels on the Bath Road would be the nearest, and presuming you really hotel virgin terminal 3 heathrow "quickest to get to", that would be by getting a taxi rather than the Hoppa or a free bus. Try this map http: Hilton london paddington is 15 minutes by heathrow express. For those who know Heathrow hotels the map on the web site linked by Joe might provide a few minutes entertainment as many of the hotels like the Premier Inn and Holiday inn Bath Road are nowhere near the location depicted on the map. The Premier Inn shown as being the closest is actually one of the furthest hotels from T3. Some cheaper hotels that don't pay commission are not marked like Travelodge and easyHotel are not marked. As Joe hotel virgin terminal 3 heathrow though there is no best closest hotel.