New City Blues

So I just moved to this city last week and honestly, it's been a real letdown. Thought I was stepping into some kind of utopia where everyone is friendly and there are rainbows at every street corner, but nope. It's like walking into a room full of strangers who have never heard of your favorite band (even though you think it's way better than that popular one everyone knows). Trying to make friends here feels like I'm trying to fit in this oddly-shaped puzzle piece when all the other pieces are perfectly round. Anyway, today I was out walking my dog and there was a group of kids playing soccer. I thought, 'Hey, maybe they'll invite me to join,' but nope. They just kept staring at me as if I had two heads (which, to be fair, the dog does have). So now I'm kind of avoiding parks and playgrounds because it feels like everyone's secretly judging my choice of shoes or something. And you know what's really weird? There’s this old lady who lives across from me. She waves every time she sees me, but she looks like she could be the grandparent of most people here. Maybe I should just start talking to her and adopt her as my official friend in town since no one else is stepping up. Anyone have any tips on making friends in a new city? Or am I doomed to be that weirdo who sits alone at coffee shops every day?