speaking as a guy with AVPD and thus with a general difficulty in doing exactly what you describe, i will say that as an adult (read: a person who doesn't get the chance to socialize in school/uni) your best bet is to join a club or any sort of group activity.
The idea of getting on an app is attractive, but keep in mind that that will bring you to meet other people in your same situation - which doesn't really help integration, since you are a person out of the local network meeting other people that are out of the local network. So it's not really the best if your intention is to "integrate" yourself in the new area.
i am into sports so joining a rock climbing course allowed me to meet other somewhat likeminded people. I also got into a group that does experimental archeology (in other words, we study medieval manuscripts about melee combat and we try to recreate what is written there in order to figure out what works and what doesn't, thus understanding better how people actually fought). That's the best kind of group activity imo, as it forces the people present to interact and discuss with each other.
In my experience going to bars and whatnot isn't really effective nowdays, since people go there to meet their friends and not really to get to know new people. But then again i have psychological issues about that so what do i know