Where you can go and what is available will depend a lot on how large/type of city you live in.
Some independent gameshops have a poster board, or some equivalent, where people forming PnP groups can post. If you've got that, it's often the source for the best experience.
Large cities will occasionally also have a forum where people can post for groups, but getting anything but DnD and Vampire out of them is quite unlikely.
There are virtual tabletop tools these days too, usually with a forum attached for people to form groups in. That is by far the easiest to get going, and often has the best choice of games, but the interplay over the net often lacks a certain something.
*
The quality of the group depends a lot more on the quality of the people involved than the quality of the game. Finding a good group is seriously hit and miss.
D&D is by far the easiest system to find groups for, but these days it is really resource intensive to get into. ie, there's a lot of expensive books to buy just for making a character. And then you have to make a character using all of them, requiring you to draw from rules spread across multiple books, thus demanding a great deal of time and study. Large upfront outlays of money and time aren't a great way to start. (Technically, vanilla D&D only requires the purchase of the main handbook, but good luck finding a group that doesn't use every book available.) Pathfinder sidesteps part of these issues by putting everything online, freely available. But there are still a lot of books for character creation, and more being added all the time.
In that sense, games from companies with low outlay are the best for starting out, such as Chaosium's Cthulhu or Pendragon, which you only need the one main book for, and both of which you have a chance (if slim) of getting a group for, or something like FASA's (now out of business, but popular enough to still find groups) Battletech, which doesn't place any demands on the player for purchasing anything at all. It is also still possible to find 2nd ed D&D groups, or even OD&D groups, both of which only require the one handbook. Vampire/Werewolf/Mage is really easy to learn, but the Storyteller system is a system built for storyfags, so you should be a storyfag if you look to go in that direction (though, as always, the group determines far more than the game system).
Please?
