Thank you everyone for your inputs! I looked into all the options and I suppose London is a very expensive city as the budget option at County Hall is 180 pounds which is US$300.
I was looking to spend much less so I settled on a place in Earl's Court for about 52GBP (roughly US$80). While doing further research, this article resonated with me:
http://www.londontoolkit.com/blog/ai...throw-discuss/
When I looked into areas like London Bridge or near the London Eye, the subway ride going back to LHR wouldn't be that convenient. True, I'm doing some backtracking by going from Earl's Court to the tourist area, then head back on Piccadilly to LHR but I'd much rather pay much less in exchange for a 20 minute subway ride to the sightseeing area in the morning.
Again, this makes sense for me and I appreciate everyone's input. Hope this helps others as well.
On a related note, now I'm considering forgoing my LHR - CDG flight and just taking the Eurostar to not waste time going out to/from the airports.
http://www.flyertalk.com/forum/briti...-eurostar.html