A few suggestions:
Portchester Castle just north of Portsmouth:
http://www.portchestercastle.co.uk/
Port Solent marina is nearby, with a good choice of restaurants and cafes:
http://www.portsolent.com/
Another vote for Fort Nelson:
http://www.royalarmouries.org/visit-us/fort-nelson
Try and visit when they are having a gun firing
Bosham is nice for a walk:
http://www.bosham.org/
The road floods at every high tide - best park in the car park!
Near Beaulieu is Buckler's Hard (nice for a walk):
http://www.bucklershard.co.uk/bucklershard/index
and a little bit further Hurst Castle - the trip out by ferry from Keyhaven adds a bit of extra interest:
http://www.hurstcastle.co.uk/
Southampton has an aviation museum - it is small but interesting:
http://www.spitfireonline.co.uk/
Can't really recommend a hotel - Portsmouth has a Hilton and a Marriot but neither are up to much, Hilton is probably the better of the two. There is also the Solent Hotel:
http://www.solenthotel.com/gallery/
If you don't mind driving there are a few good local country pubs:
http://www.welovelocal.com/en/se/eas...n-so318de.html
http://www.welovelocal.com/en/se/eas...n-so318dn.html
http://www.theshoeinn.moonfruit.com/
Cheers
Chris