Where in the UK are you from?
I would suggest New York but that is because I like going to places with a different culture than my own. If you aren't used to cities than both are going to be a bit of a culture shock. New York is the most like London of any of the American cities I have been to but is still very much its own place (planet..lol). You will most likely get the chance to visit London again in your life so I would go to New York. Afterall, both places are going to be cold in Novemeber so you mineaswell be cold in a different country..lol
Things people tend to see:
The Statue Of Liberty
Ellis Island -
http://www.ellisisland.com/ (it means less to UK people than to us but it is still an important part of world history and a nice building)
The Empire State Building
Ground Zero - depressing for most but again, important to world history and somehow makes it more 'real' to see it.
All of which are stops on the tour busses, btw. The tour bus tickets are usually good for 24hrs so if you buy it at noon it is good until noon the next day and you can get on and off.
There are loads more things but again, it all depends on what you are intersted in.