Portsmouth has the HMS Victory (Nelson's flagship), HMS Alliance (submarine from WW II that was modernized after examining the German Type XXI u-boats), Mary Rose, the RN Museum (read Colin White's two books: The End of the Sailing Navy and The Heydey of Steam as primers before you go and it'll enhance your visit), the Royal Marine Museum and finally the first British ironclad, HMS Warrior. Plenty of Parker Hale Enfields on board her. There's also the remains of a Roman castle nearby too.
If you get to Winchester, there's four military museums including the Royal Green Jackets. They're descended from the 60th (Royal Americans/King's Royal Rifle Corps), 95th (Rifle Brigade), 43 & 52 (Ox & Bucks). The Light Infantry Museum is there as well as the Royal Ghurkas and the Hampshire Regiment.
If you go to York, besides walking around the wall and seeing the Keep, there's also the Regimental Museum, Yorrick (sp) Viking Center, York History Museum (may have the name off) that was converted from Debtor's Prison. Cadbury Candy is nearby too but I don't know if they're open for visits.
If you're in the midlands, visit Leeds for the Royal Armoury Museum. Guns galore, old & new. Arms & Armour.
If you're in Edinburg, walk the Royal Mile. See the castle which houses Mon Megs (mother of all cannons and if not the mother which it isn't, it's certainly huge), two regimental museums. On another hill is the unfinished parthenon. Becareful of your personal possessions as I've been warned of the Scots (never had trouble myself but then again I look poor when I travel).
London. Oh, for a couple of months there. You've got the Imperial War Museum (20th Century) which is a couple of days. The light cruiser HMS Belfast is open to the public (WW II 12 x 6" gun). Victoria & Albert Museum, British Museum (like our Smithsonian), National Gallery (if you like paintings & art), booksellers (near Picadelly) galore. The Royal Army Museum is also there (they have a facismile of the Royal American uniform on display when I went). If you get to Herndon, the RAF museum is there. See a Ju-87 Stuka Dive Bomber, HE-111, JU-88, Me-109, Spitfire (several), Hurricane, Wellington, Lancaster and other famous planes for days bygone. Worth the visit.
BTW, I've never been to the Royal Armoured Corps Tank Museum in Dorset. It's suppose to be well worth the day and they have a running Tiger I tank.
Eating in pubs is cheaper than restaurants. Carry-away (might be a different term) is cheaper than eating in-house.