There's a couple of hotels I can highly recommend in Alverstoke on the outskirts of Gosport. Just across the harbour from Portsmouth.
The Alverbank Hotel. Used to be a royal hunting lodge.
The Old Lodge Hotel. In the village centre next door to an old church.
Both very nice. I've stayed at both and the service is excellent. You have all the sites and sounds of the maritime museums:
The Submarine Museum - Gosport
Explosion, The history of Naval Firepower - Gosport
HMS Victory - Portsmouth
The Royal Marine Museum and D-Day museum in Southsea.
Portsmouth and Southsea are accessible via the Gosport-Portsmouth ferry and if you're not interested in all that lot, the beach in Alverstoke is nice and a couple of miles long with views straight across to the Isle of Wigget!!
Oh and Gosport is also home to Europes largest private marina if you like sailing boats (Camper & Nicholson).