The absolute best way to easily tap into a Social Circle is through sports that both women and men play. Tennis, netball, volleyball, bad minton, yoga.
You join a local club, tennis social or whatever. Don't go there and be sleezy, go and get really good at the sport. Within 3 months you'll have a social circle centered around a shared activity. It really is very easy unless you've got social anxiety.
I've been playing tennis since I was 8 years old. I played for my high school team all 4 years of high school. I didn't play during college. After college graduation, I returned to the sport. I'm a solid player and have beaten ex-female NCAA tennis players despite the fact I didn't play NCAA tennis. I would not recommend tennis as a sport for finding dates, not at least until you are about 40.
As an adult, I've played at both public and private courts. At both public and private courts, you will rarely see women in their 20s/30s playing a singles match together. In most cities, a lot of the private tennis facilities are located in more suburban, family oriented areas which are not close to 20s/30s childles singles. A single woman in her 20s/30s would be a bit of an oddity at a private facility. At public courts, when a younger woman is playing tennis, she's typically playing with her husband, boyfriend, brother, or some other guy.
On the rare occasions you see two women playing a singles match, definitely approach. I have gotten dates this way but it is rare to do.
When women turn 40 or so, tennis becomes a more viable to pick them up at private courts. It's common to find 40 something divorced women at private tennis clubs. These are usually upper middle class and higher women that got into tennis with their exes remain playing tennis or they are just picking it up to get a hot, post divorce body.
Volleyball is a much better option for picking up women. There are often co-ed sports leagues for volleyball. Sand volleyball is a great way to meet women if you live in Florida, Southern California, or in an inland city with a good sand facility. A lot of ex-indoor high school and college volleyball women will keep playing as adults. Volleyball culture is a little more social than tennis' culture.