I've similarly not made close friends in the city we moved to, but I haven't tried very hard to. I'm happy with things as they are, even though most of my friends are overseas or in different cities. I'd see them a bit more often if I could/if it was easier to, but I don't feel that motivated about developing new friendships. I have made friends here but I tend to get along most easily with men and the friends (they were closer to acquaintances) who I worked and studied with had partners/wives. It would've made it awkward meeting up with them in the same way I might meet up with a female friend, so I've pretty much taken a step back from those friendships and let them slip away. They're still on my social media but that's about it.
I did join a gaming group years back but it didn't work out (I think I may have caused offense saying something to another group member after a total party kill (with the exception of one player who wasn't there that night), one or two games into a Cthlhu campaign. They had little tolerance for any comment from me (no matter how innocuous) and their place was really hard to get to/a lot of travelling, so I just accepted that they didn't want to game with me anymore and moved on from it.
We had a gaming group going here recently, but players cancelled a lot and there was only one actual game before one took a hiatus, and another dropped out, and we haven't re-established the group again yet. By comparison, our old tabletop group was going for around 10 years.
As for older/younger people, I don't know. I haven't had many older friends beyond a few years, but most tabletop gamers have seemed around my age group (I'm late 30s now). I live in a college city and most younger people seem like they live in an alternate universe that involves drinking and being social all the time in ways I tend to avoid out of preference. I guess I just prefer hanging out with who I want to and doing what I want currently. Maybe that's a sign I'm getting old or just that I'm an introvert.
I know that isn't too helpful in terms of suggestions. If you want to meet people then I agree with the suggestion/s to take the initiative. Sometimes friendships happen but usually someone has a hand in creating them (for instance, a school if everyone is thrown in there together or a gaming group, if someone forms it and others join). If you're a gamer you could create a group or join something where a number of people have something in common (NaNoWriMo's coming up in November and a lot of cities have meetups). There are other things too.