I would advise against Hard Rock if your child can't stand waiting. I can't either! I tried to go to Hard Rock last summer around this time on a Friday and people were queuing up down the street waiting to get in. Needless to say, we gave up!
If you are looking for that sort of American food, there is a TGI Fridays in Covent Garden. I've never been in London, but it's good in the US. There might be a wait there as well though. I think you might find it hard to find somewhere on a Friday without a wait, but you can probably find a place where you don't have to wait too long. There is also a place called The Diner in Soho. I've been to the one in Camden and it was really good. It reminded me of an authentic American diner.