Try
http://www.innkeeperslodge.com/lodgedetail.asp?lid=74
It's a hotel attached to a big pub in Snaresbrook, east London. It's about a minute's walk from Snaresbrook Tube, which is on the Central Line. You'll be at Oxford Circus in 20 minutes from there but it's one the edge of Epping Forest so you can take a nice walk before you head into town. Also, Wanstead, which is the area it's in, has lots of nice restaurants and funny little shops to poke around in.
Alternatively, there are lots of hotels in Docklands which do good deals at weekends. Some of them overlook the river – The Tower Thistle hotel in Wapping overlooks Tower Bridge and sometimes does good deals. You can walk along the river into town from there and it's beautiful at night.
Good luck, hope you have a great time. x