It's a bit of a way out, but Hatton Cross tube station is very close to the end of the runway, you'll pass it most likely on the way over, and you can have a few jets roaring over your head in one direction or another. There the walkway between terminals so you can go and see the C gates with the big aircraft going out on the train and then back on the walkway (DO NOT ATTEMPT TO USE THE TRAIN TO RETURN, you'll be delivered to Arrivals).

There's a great I Spy Book of Airports which its worth looking out for as it gives a bit of a framework to look at things. You may want to check in at the desk and explain what you're doing to the staff as they sometimes have giveaways.

The nose cone isn't all that exciting. Concorde itself is often visible as you taxi, and to be honest extending the day to go to Brooklands to see a real one may be a decent option.