The fireworks over the London Eye are where all the midnight action is. The best hotel to stay at if you want to view from your room would be the Swisshotel Howard - http://www.swissotel.com/london/index.htm

However, you could stay anywhere near the river eg stay at the Travelodge South Bank (http://www.premiertravelinn.com/pti/home.do) and just walk over to the North side of the river opposite the Eye.

A few hundred yards further away, but excellent, is City Inn (http://www.cityinn.com/london). If you like Hilton Trafalagar, you will like this hotel.