In your opinion, where is a good place to extend one's social network?

Question

To make meaningful alliances/friendships/partnerships etc other than one's usual/normal places

Answer 1

Church

Coed recreational activities such as volleyball, baseball which may be sponsored by Y, church, college, or community rec centers.

Hiking and biking clubs

Craft clubs where people come together for self help and joint sales sessions

Volunteer groups that work to solve problems together such as home building, visiting the elderly, etc. or in places with people contact such as library or community information

  You want places where people talk to each other (not tennis for example, for filing or editing in a back room) and especially where people present already share interests and have something to talk about.

Answer 2

I think that joining a club (photography, hiking, whatever...) is the easiest route.

You're sure to meet new people with similar interests to yours.  Regular meet-ups ensure that you'll see them again and have at least that constant contact as a basis for a friendship.