If you haven't already found it there is a fantastic website called
www.tripadvisor.com. I use it whenever I need a hotel. It gives you reviews by other travellers and tells you how popular it is. Some people even post photos of the place from staying there. You can also book hotels via the site once you've done your research.
I live in London but occasionally stay there overnight. Given the exchange rate of dollar to pound you're going to find it very expensive. Even the flea bitten drug dealer prostitute hotels are going to charge you £50 a night ($100). The average price for a hotel in central London would be £150 - £200 ($300 - $400) a night. The five star hotels such as the Savoy, Claridges etc. charge a minimum of £350 a room ($700).
I hope you find somewhere suitable but may I suggest staying outside the west end and getting a better hotel for your money and travlelling in on the tube?