Vader and the droids

Ya know, that's acually quite a good point there KJ. I never thought of that. That kind of shows that R2-D2 will return to Tatooine in Episode 2 and/or 3, as he wouldn't exactly know his way around just because of where he went in Episode 1. Perhaps he'll see where Obi-Wan's home is and that's how he knows where to go.
Then again, perhaps Leia just gives him maps of the planet within the data she puts inside him.

I think that might be an interesting bit to keep in mind..I think it is very possible that R2 remembers Tatooine quite well.

What about other planets? Do you think he may go to Dagobah at some point? Did he kind of lead Luke towards Yoda in TESB, or was Luke leading the way?

I don't know about Degobah but back to Tatooine, Leia wouldn't have known where Obi-Wans house was. He was a Jedi in hiding so I don't think he would tell people his address.

So how did she know he was even on Tatooine? Did she just drop R2 onto Tatooine, just because it was right below them?

Bail Organa would have known he was on Tatooine but not the exact location.

Perhaps Bail Organa did know where Ben lived, they were very good friends. Maybe OB1 told him in case of some kind of emergency with Leia. How else would Leia have found him at she made it to Tatooine?

Good points there. Bail Organa could indeed have some connection with the knowledge of where Obi-Wan lives. They were certainly friends after all, as they fought alongside each other during the clone wars.