The droids didn’t randomly land in the planet Obi-Wan was in, and didn’t randomly land close to his home either. That’s all text for the original film. They knew Obi-Wan lived somewhere around there, R2 I think even knew exactly where. “Secret mission, what are you talking about?!” (as R2 heads in a particular direction). He also escapes at night and has a specific place he wants to get to, which curiously (obviously!) is closer to Obi-Wan’s home since he shows up.
Hopefully it becomes obvious that R2 programmed the pod to land there, near Obi-Wan. And Obi-Wan lived next to Luke on purpose. I really, really fail to see a coincidence. And I’ve tried.
There’s that too. R2 remembers everything and far more than he let’s on. He’s been to Tatooine before and for all we know he could’ve been given instructions by Leia to where Obi-Wan lives. I don’t think she’d randomly give him the mission to complete without any help on where to go. So it’s not out of the realm of possibility he knows where to go through experience and help from Leia.