Darling, I think you are over thinking this.
Honestly if you had said to me "let's play super mario bros" I probably would have said sure.
Ok, places. Are there any nice parks where you live, or any other places to take a stroll? Walking is a wonderful past time. It gets you outdoors and moving and while you're moving your body your brain is nice and active, meaning conversation should come easily, and if it doesn't there should be plenty to inspire you to talk about or enough to look at to keep silences comfortable. I honestly at this point can not think of a better suggestion for you at this point.
How to move on from casual convo... You have to stop worrying about looking like a doofus, or a weirdo. In your gas station example you could have followed up with "I have enjoyed our chat. Is there any chance we could have another?"
'People are never perfect but love can be. People waste time looking for the perfect lover rather than creating the perfect love' - Princess Leigh-Cheri from Still Life With Woodpecker.