I have moved several times. Usually I make great aquaintances at church that then develop into friendship.
I get involved at my kids' school which opens up the circle of potential friends.
Find a hobby and get involved in it through local adult classes. Find a book that looks intriguing and ask some ladies to read then come together to discuss...don't make it seem like a looooong commitment. Read one and see who is up for another.
Find a friend to exercise with. My best friends have come through this. We'd go in the early morn. while hubbies were still home. I have moved away from my 3 bestest friends that were made through morning exercise. We still keep in touch, get together as often as we can. ANd now train for races on our own then come together for the actual race day. Soooo fun!
I host occasional girl's night out at my home and my hubby takes our 3 kids out for a few hours. Having it at home keeps things cheap...everyone brings a food item to share and we sit around chatting and occasionally playing games. Mainly everyone likes to plunk their butt down on the couch,eat,visit and enjoy visting with friends without interrupions. These are not my bestest friends but friends in our area that I enjoy hangin out with...who knows ...relationships could develop into a closer friendship.
We also have a large yard with pool so we invite people over to swim during the summer months. It is very relaxing, gives moms a constant activity to do with their kids in the summer and we get to visit and get to know eachother better. I also try to invite ladies that are new to the church,school and neighborhood. if you lived closer I'd invite you!
Good luck with making some lasting friendships. I truly believe friends are important for our heart and soul.(and sanity!!!)