The main fallacy like you see in this thread is that it everyone thinks it needs to seem unintentional, so that you're not "needy".
This is a big fallacy.
Don't try to make it seem coincidental, instead make a real effort. Here 3 steps on how it works
1. Go to meetups, try out lots of new hobbies, connect with everyone on facebook immediately if you click. Do it with guys and girls. Some will be awkward, but most don't care and just say sure and connect.
2. Then keep the conversation alive a bit and meet up with them around the activity or meet up you met, ask who is going to the next meet up, be it hiking, exchanging info about cryptocurrencies, ruby on rails or whatever. You can also make chat groups on messenger with 10 people or so
3. Be a value giver, be an organizer, be the one who knows what's going on, people gravitate to people like that.
4. Doing this is not needy as long as you are a value giver. However, don't ask people all them time for value, don't be a value drawer too often.
5. Keep it lighthearted, don't become pissed if people don't join your meet up or son't reply. This is needy behaviour. After a few months, you should have 100 people in your new social circle, so what do you care if one doesn't come
As you can see this takes effort, but this is a recipe of how you can build a vibrant social circle for you within a few months time every time you come to a new city.
Most people don't do that, because they are so scared of rejection. But what do you care if 20 people don't want to connect with you when a 100 do. There are always people who want to stay for themselves, are weird or asocial.