You can always join a local playgroup...:) There are so many in Jax!! Go to Yahoogroups.com and do a search, or try meetup.com, also.
You could try stopping by your local park and chit chatting it up with other parents...great way to get some playmates and friends...
If your not looking to join a playgroup, you have fun things, like--mall play areas, the beach, parks, YMCA, storytimes, nature walks and discussions at varies places---If you need more ideas, just email me--I have lots! :)
I own a playgroup here, also...check it out!
http://groups.yahoo.com/group/jacksonvillekids/