You can but it costs, usually, over a £100 per ticket for the private access tours and they are usually linked in to other places such as Windsor or Bath. Not many people can afford that. Avebury is much more my sort of place and you only have to pay to park the car if you're not in English Heritage or National Trust when it's free.
They are both half an hours drive from me so I'm spoilt for choice!
Taz x