apart from london where there is loads of tourist attractions....
Oxford or Cambridge (oldest university towns) are classic places to visit for tourists, also maybe york and yorkshire dales. there are many other citys in north of UK - Liverpool, Manchester, Sheffield and Leeds - never been there so can't comment on whether worth a visit.
if you're into the outdoors - the lake district/cumbria
there are plenty of stately homes/castles if you like "history" and Windsor castle is open to the public (just outside london).
checkout
http://www.nationaltrust.org.uk/main/placestovisit/visit StoneHenge and salisbury is close by.
Canterbury Cathedral
i particularly enjoyed Warwick Castle - its restored castle with historic recreations and knights jousting tournament etc (ok if weather is good)
visit Nelson's ship the "Victory" and Henry 8th's "Mary Rose" at Portsmouth .
you could visit shakespeare's birthplace Stratford-on-Avon) and catch a play.
devon/cornwall has plenty of quaint places to visit (eg. Clovelly, St Ives, Lands End) primary attraction in cornwall is probably "the eden project"
http://www.edenproject.com/ or visit the "mayflower steps" in plymouth where the first settlers left to go to the US.
if you're into rollercoaster ride attraction parks "chessington world of adventure" (near london) or "alton towers" (staffordshire) are the best