First things first...

Do you have the right to stay so long? And if so, do you have the right to work?

I have an American passport which, I believe, allows me to stay for up to six months. I am still looking into my right to work.

See: http://ukinusa.fco.gov.uk/en/about-us/faqs/living-working/work

Note especially:
Application for the work permit must be made by the prospective employer in Britain. Individuals cannot apply for a work permit on their own behalf. Applications must be made by the Britain-based employer.

That 6 months will depend on satisfying an immigration officer that you can support yourself whilst in the country and that you're not likely to overstay. It is very unlikely you will have the right to work whilst in the UK. The rules on working as a non EU national are extremely restricitve.

I am still looking into my right to work.

Unless you are top of your profession, willing to invest a large sum of money, want to pay for a course at a university/college or have blagged a transfer to the UK through your US company then your chances are somewhere around zero.

Note that if the UKBF even thinks you are going to work without a suitable visa then you will be denied entry to the UK

"If I live in London is using Craigslist the best place to find living arrangements"

Definitely not, full of scammers.

if the immigration/visa stuff works out:
1. stay in london
2. try http://loot.com/property/bedsits-and-studios for living arrangements.

I think a large part of the quesion is how much money you have to support yourself (assuming that you cannot work - which seems the most likely). London is VERY expensive. Will you be able to afford the cost of even a studio actually in London? (And no, Craig;s list is the worst way to find anything - until you are actually on the ground and can view the property in person. Even then be careful - a young colleague of mine nearly "sublet" an apartment of someone who was on vacation and didn't know her ex-boyfriend still had a key. Luckily she met, the super, he asked what she was doing in X;s apartment and she said - but the apartment belongs to y. the super cleared it up before she had handed over more than $1800 for the first month.)

My kids both got their graduate degrees from a UK universities and got a UK work visa(which cost close to around $700USD) for two years and STILL cannot get a job over there with specialized degrees so don't think it is easy to get a job there.London is horribly expensive to live in so do your research before you go.

If you are planning on doing this this summer I think that you should be prepared for massive crowds between the Jubilee and the Olympics along with the usual tourist crowds-everything is going to be packed!

Hello,

There are very few categories of work visa open at the moment, the highly skilled migrant program has closed so you can't get a visa and try to find work once you are here. I'm sorry but there simply aren't any visa categories applicable to you - or helpful as for example there is a Tier 5 temp charity worker visa, but it has to be unpaid work.The only other visa category still open (unless you happen to be a minister of religion or something!) is the skilled worker, for which you need a definite job offer from an approved sponsor firm, AND they must be able to show that there are no people already settled in the UK able to do the job. I have known one firm import an obscure software specialist via this visa but it took a lot of jumping through hoops. It also involves the firm in expense and faff and no way are they going to do that for a temp.

Forget any ideas about working illegally - employers just won't take the risk. The only time this happens these days is for family members/friends in places like ethnic food restaurants etc. working 'under the table' just doesn't happen here now. There are 1000s of legal workers - don't forget the whole of the EU is entitled to work here - who will do anything for minimum wage.

So..after all the negative, here's the positive. You can visit for up to 6 months without a visa but you will need to show that you have the funds to support yourself during your stay. In London/out of London? That's personal preference. London is expensive. There are other major cities that have a lower cost of living if city life is what you want. There are of course cheaper areas in any city but there's always a reason they are cheaper. Some are just grotty; some are dangerous.