Not got any good recommendations for hotels because I've rarely stayed in a hotel in London - the only 'budget' one I've stayed in was the MIC near Euston station, which was alright.
In terms of bars and clubs, depends what you like obviously, as London has a great gay scene. If you like the 'harder' clubs then you probably want to check out venues in Vauxhall - the best bet though would be to check out the online edition of QX magazine (gay London listings mag) to find out what's on and where on the different nights, and it'll give you some idea of what sort of place it is (e.g. indie, cheesy pop, house, cruisy).
In terms of Museums, I'd recommend the British Museum and the Natural History Museum, and check out the National Portrait Gallery and the Tate Modern too.