D.B.
HI H.,
I don't know anything about your area, but in general, I'd offer the following:
1) Most 2 year olds don't play a lot with other kids. Parallel play is much more common - they sit in the same area and do their own thing, rather than engage directly with another child. That doesn't mean there's anything wrong.
2) It's okay to be shy.
3) Go to the children's wing of the public library. Look on the bulletin board for play groups, or see if you can put up a flyer letting other parents know that you are interested in setting one up. Ask the children's librarian what free programs they have - story time, puppet shows, visiting authors, arts & crafts programs, computer fun, whatever.
4) Find out if there is a Newcomers' Club in the area. When I was a new mom, it was a great way to meet up with other new families in a variety of interest groups - there were couples' programs, play groups, museum trips, etc. We met in each other's houses, rotating from home to home, so each family only had to host every 6 weeks or so.
5) Check with local museums to see if they have kids' programs - a general children's museum, a science museum, the art museum, and more.
6) Check the craft store - sometimes they have age-appropriate, hands-on craft programs with supplies at a very limited cost. They are trying to build a customer base by showing you things that kids of different ages can do.
7) Check with area churches, synagogues, mosques, Jewish Community Centers, YMCA/YWCAs and ethnic social agencies to see what they have. Not all of the programs are just for people of that religion or ethnic group. They are often free or very limited cost (just enough to cover snacks and juice, for example), maybe more if there is a trained activity leader.
8) Groups like Gymboree have a cost, but they have age-appropriate activity groups.
9) Is there a children's store or resale shop near you? Sometimes they know of programs or have a public bulletin board.
10) Call a few local preschools and see if they have a "mommy and me" program once a week. Everyone there is interested in meeting new people, and the schools hope these will be "feeder" programs for their regular programs for kids 3 and up.
11) See if your local gym offers classes and babysitting. A lot of them do, to make the classes accessible to parents with young kids. There's a play room, and the kids can hang out together with a sitter while the moms take an exercise class or work on the machines. You'll find that some people go on the same days, and you wind up getting to know each other.
Good luck - don't give up!