I've flown into Gatwich (GTW) many times. There is a train that leaves from the terminal to Waterloo station in London for I think about $10-15 one way, then you can use the underground to get around.

The first time my wife and I did this it was really simple to figure out, and fun!

If you do chose to rent a car, Gatwick is about 30 miles south of London proper, so you have some non-city driving time to get used to driving on the "wrong side of the road" if you've never driven on the left hand side before.

But I don't recommend a rental car if you are just seeing London. London is great fun and so easy to get around in just using the underground, buses, and the occasional taxi.

Have fun!

Cary