Tennis' history show that it was the sport of choice for kings and royalty.
Today, though, it still has that reputation. I think tennis appeals to a lot of people, and a lot try to play it. The sport is actually much more difficult than it looks and it generally isn't associate much with athletes so much as it is with intellects because, let's be honest, you have to be smart in order to play the sport well. It's a technical sport which means that because the motions aren't really natural for the body, it takes a lot of skill and practice to do well.
As for the "snobby" part, I learned to play at my city courts and don't play at clubs or anywhere else where I'm required to pay. I don't see the reason to as I have access to public courts. I learned tennis through my high school team (and we also practiced on the city courts) and met a lot of different kinds of players from all kinds of backgrounds. It is a more expensive sport to play, but it doesn't have to be. Court access can be free and balls aren't that expensive. Any kind of sports clothes will do and racquets can be as cheap as USD $30. Of course, as you get better and play more important matches, the expenses do come.