I want to start a trip going from the UK to North America. I remember when I went years ago we had to fill in a form and give an address of who we were staying with. What do I do if I don't have an address, and just coming to travel around?
UK takes part in the visa waiver program. Only thing you have to do is to apply for an ESTA (visa) online. Its not very expensive. About 2 years ago it was 14 USD.
Go here for your ESTA: https://esta.cbp.dhs.gov/esta/
You are right, you have to enter an andress, but thats only for where you will be staying the first night after arrival.
I am pretty sure you will have something arranged after the long flight to get some rest and continue on the next day. Even if you have a connection flight to another city, enter the place where you will be staying at the form.
The same adress need to be entered in the customs form, which you will get during your flight to the US.
And thats it. Its pretty easy...
The ESTA visa is good for up to 90 days. if you want to stay 91 days or longer you have to get a visa or leave the country and come back the next day would probabyl work too. But make sure you don't exceed the date marked in your passport stamp once you arrive.
I think it really depends how how long you are planning to stay. This site should be useful in finding what category you will fall under: http://travel.state.gov/content/visas/english/general/all-visa-categories.html