But, I took a modestly more expensive "Inner Stones" tour a few months ago and lucked out being selected to be fully alone for a minute. It was a profound experience being in the middle of such a historic place.
Highly, highly recommended!
It also has a pub, a restaurant, a gift shop, a museum founded by a marmalade magnate, and if you're really rich you can buy one of the houses inside the circle.
Generally a happier experience than Stonehenge.
If megalithic rocks are your thing there's also the nearby West Kennet Longbarrow, which is far more likely to be deserted, especially at night, although if you go on the quarter days (nights) you'll probably meet weirdly-dressed people lighting candles and throwing spells around.
During the the 1980s and ‘90s there were regular clashes between new age hippies and police stopping them from reaching Stonehenge during summer solstice before public access was allowed.