Via Central London is by far the easiest way from Nottingham to LHR. The bus is less comfy , even being diplomatic , and Nottingham to Reading will require a change at Birmingham New St and onto a bus at Reading. The Nottingham to St Pancras train is reasonably fast . comfortable and usually reliable. There are two Premier Inns on Euston Rd a few mins walk from St Pancras , which are quiet , decent and and very convenient for Tube stations to LHR in the morning , (provided you are not too loaded with luggage )
Euston Rd isn’t far from tourist central for pubs and restaurants , if you want a real British boozer , basic but excellent beer , there’s one two mins from Euston and some OK Indian restaurants nearby. Bloomsbury , just behind the Premier Inns , has some nice old pubs , places to eat by the Brunswick Centre and is a pleasant place for a wander with nice architecture and garden squares.