Flats??

I am going to London in 2 weeks to look for a flat in the Chelsea area. Does anyone have any suggestions for me. I am moving from Las Vegas and want to make sure we live in a  good area. 

Chelsea is pretty much all nice, but expensive.  Public transport can be a bit of a PITA, but if you're working/studying/whatever in the general area, it's not as big of a problem. 

Great-- What do you think is the best way for me to find a flat? I would like to do it on my own without having to use an estate agent and pay those fees. Are there local newspapers that would have this kind of information?

Yes, pick up a copy of Loot (listings paper) and also look at the Gumtree website.

Try these websites:
www.rightmove.co.uk
www.findaproperty.com

Many estate agents manage the flats they rent and not all have fees/commission for renting other than a charge for a credit check.

Try these websites:
www.rightmove.co.uk [nofollow]
www.findaproperty.com [nofollow]

Many estate agents manage the flats they rent and not all have fees/commission for renting other than a charge for a credit check.

I second this, these two have been great for at the very least letting me know what the prices are.

Be sure to ask the agents what else they have on their own sites or get the address and look it over yourself BEFORE you see them to look at something you found on either of these sites. We did so and found a fantastic 3 bedroom at a great price that the agent had thought we wouldn't be interested in. We took a look at what she wanted to show us and then hit her with the one that I found on their site, best move I've made so far.