It depends where you're staying - the Solent Hotel in Whiteley is about a 5 - 10 minute walk. Having never stayed there, I don't know how much it is to stay:
Hotels in Hampshire | Solent Hotel & Spa, Fareham
If you're staying in Southampton, then it's quite a hike to get there. The nearest station is Swanwick, which is about a 25 minute walk...on a good day, although there are taxis, but again I'm not sure of the costs. Trains can be taken from Southampton Central - check the trainline.com
Alternatively, the 28/28A bus goes from Swanwick Station to Parkway in Whiteley which is just down the road from NATS
http://www.firstgroup.com/uploads/maps/Route-28_28a.pdf
Timetables | Portsmouth, Fareham & Gosport | First UK Bus