heaps. National Theatre, London Eye, aquarium, Royal Festival Hall, National Film Theatre, Oxo Tower, Millennium Bridge, Vinopolis, HMS Belfast, riverside pubs, upmarket restaurants, Design Museum, lots more.
The area around the Royal Festival Hall is really nice on a sunny day. There are upmarket outdoor bars (or you can do as I do, and buy a pint inside the NFT and take it outside - it's cheaper that way!). There's often free entertainment in the area. (There's a 'Brazil' theme currently taking place) or you can simply try to work out how to get inside the 'rooms' of Jeppe Hein's artwork without getting wet!
http://www.southbankc...pearing-rooms-1000000
The area around HMS Belfast (Tooley Street) used to be really grotty, with little more than a collection of derelict warehouses - but it's all been smartened up to incorporate the stunning City Hall, which hosts free exhibitions:
http://www.london.gov.uk/city-hall/exhibitions
A good way to get across to the south of the river, and to travel around it, is to use the frequent RV1 bus service from Covent Garden:
http://www.londonbusroutes.net/times/RV1.pdf