Go to London if you can. London is the best. With exceptions of one or two, all museums and major galleries in London are FREE!!! Woohooo! Visit as many times as you want and if you are an art lover and want to see those masterpieces over and over.....it's fantastic....You can even borrow an easel to draw or paint in the National......Now that is CIVILIZED!! Gotta love the British for this!
Art galleries, start with the Tate Britain for things like the permanent Turner exhibition. Tate Modern is what it says =- modern art, mostly 20th century. There is the national gallery which will take all day but has a superb collection and you should try some of the smaller specialised galleries as well. Basically whatever you want it will be almost certainly be in London somewhere.