What kind of art do you like ? And by 'art' do you just mean painting or decorative art in general?
The Victoria & Albert has a great range of galleries & usually has a good exhibition on - it's a museum but it does have a limited range of painting art - good stuff though, and you can pop round the corner to the natural history museum/science museum when you're done.
Or Tate Modern has some great stuff (as well as some crap) and the building it's housed in is a work of art of its own (a fantastic converted power station - there's usually an exhibition of something calming in the turbine hall) - and it's right across the river from St Pauls so you can 'do' the architecture stuff too.
Or Tate Britain has loads of great 'traditional' paintings and you can check out Parliament/Westminster Abbey a short walk away.
And there're one or two pictures by the odd Italian in a poky little place on Trafalgar Sq, and a few knick-knacks and the odd dead Egyptian in some building hidden away in Bloomsbury - nothing of any great interest of course, London's a bit short on art galleries- names of the places temporarily escape me .....
