Where are you from, anyway? Things like food (variety) will be no better in London than New York or LA. Music (classical) too, probably.
If you get the chance, I'd definitely see a play at Shakespeare's Globe one afternoon. You can do the South Bank walk from there, or go to the Tate Modern, which is very close. If it's at the end of September, I also will be very close.
It will be prom season at the beginning of September (no, not acne and poorly fitted dinner jackets...) but tickets will be hard to come by.
I second the sightseeing comment above and was going to put that in my earlier post. What's the point of going to Buckingham Palace and standing at a fence with a few hundred others and trying to look in. All you need to see can be found in pictures - it's just the size that is impressive in real life I expect.
There are also many, many places to see live music (all types) virtually every day, along with a lot of night clubs.
Definitely visit Speakers' Corner in Hyde Park - it can be hilarious and mind-blowing. Free speech and all that.
Expect some anti-war/anti-US & UK presence in Iraq/Afghanistan views though. An unrelated, similar expression of free speech at a homecoming parade last year may well lead to riots this summer, if the papers are right.
Edited by aameerp - 6/5/10 at 12:59pm