How about bigger shooty gunny things in the big fort behind my house. Royal Armoury at Fort Nelson is a good day out and it's free! Do a lovely Sunday roast for a reasonable price. Fort Nelson | Royal Armouries
D-Day Museum on Southsea front
Royal Marines Museum at Eastney
Royal Naval Museum
RN Submarine Museum (on the Gosport side of the harbour)
Fort Nelson on Portsdown Hill (as earlier post)
The Royal Armouries Museum at Fort Nelson takes some beating, especially as it's free. For something different, try the Explosion! Museum of Naval Firepower at Gosport, across the harbour from Portsmouth. It is on the site of the old RN Armament Depot at Priddy's Hard and incorporates some impressive Victorian architecture. It has everything from a Polaris A3 ICBM and a nuclear bomb to heavy guns, missiles, mines, torpedoes, anti-submarine mortars, depth charges and small arms.