C3PO has a bad memory. This is clear from ANH. Luke asks him if he has been in battles, and 3PO replies "Several, I think. I'm not very good with such things." And that makes sense. As said, you wouldn't want a protocol droid with a good memory for the people they meet. In addition, Anakin builds him out of spare parts from a junk yard.
R2D2, on the other hand, seems to have a good memory (and is built by a royal family for their personal starship). He does remember Tatooine. When he and C3PO arrive on tatooine in ANH, R2D2 takes off right away. C3PO asks him where he is going, and why he seems so convinced that the village is that way (and then gets upset with him for being "technical"). Later, once on the Lars farm, R2D2 heads off asap to exactly where Obi-Wan lives. It's clear, now, that he knew where he was going. It's not like Leia had enough time (or even the knowledge) to instruct R2D2 on exactly the location of Obi-Wan Kenobi on Tatooine. But she does seem to know that R2D2 knows the way, seeks him out, and gives R2D2 the death star plans, assigning him the mission to get them to Obi-Wan, R2D2's prior "master". In fact, it's even possible that the whole reason the droids are on the same ship as Liea in ANH is so they can lead her to Obi-Wan on Tatooine.