When the football is on I'd avoid a 'drive' into Newcastle at all costs! It can be a nightmare.
You can get the Metro in all the way to James' Park/Haymarket from the airport and Samson will probably drop you at the Metro if you let them know (there are two stations at the Airport - one at the terminal and one not far from the Southside Aviation).
The City Heliport is well sited for James Park. Not overly suited to Public Transport - 5 to 10 minute walk or a very short taxi hop been practically on the edge of the city centre (5 mins from station) If you do go in the only real approach is from West/South West along the River so bear that in mind for wind. Its roughly a 3 acre site right next some big Gasometers which stand out well - a quick look on Googleearth will give you a heads up. In any case - Martin at Eagle Helicopters will want to brief you prior to arrival. Depending on your experience level you may want to keep the R44 fairly light to give you a good margin.
I cant comment on the Hotel as I don't know it.
Enjoy the game!
'Big Sam' used the heliport when he first joined Newcastle. Owen also uses the Heliport.