Perhaps it's at a local park. You're walking your dog and their dog runs up to yours. You start talking about your pets, their names, and how they behave. As you walk together through the park, you discover that you both grew up in the same small town, which leads to reminiscing about local places and memories.
Another idea is a first meeting at a book club. You both pick the same book to discuss that day. As the discussion progresses, you notice how passionately the other person talks about the themes in the book. You chime in with your own thoughts, and there's a great exchange of ideas. After the meeting, you continue the conversation over a cup of tea, finding out more about each other's interests in literature and life in general.
One idea could be a chance encounter at a coffee shop. You both reach for the last blueberry muffin at the same time. There's an instant connection as you laugh about it and start chatting. You find out you have a shared love for a certain type of music, and before you know it, you've exchanged numbers.