What exactly do you intend on seeing/doing if you do come to the UK? Going to London for the sake of going to London seems a bit silly to me, unless you have specific goals whilst being there.
I will say this, though - if you do decide to come over to the UK, keep to just one or two places where you might stay. It's a common misconception in the US that the UK is a small place, which by comparison it is. However, if you're not careful, you could spend half your time here travelling around and not actually seeing/doing what you might enjoy.
But yeah, elaborate on what you want to do when you get here, that way people will be able to offer other suggestions as to what you should do, where you should go, etc, providing you with more choices.