Because they wanted to avoid the Sith sensing their presence
Remember, Anakin was born off the Force; his powers were not what the Jedi expected to be. Qui-Gon even says that Anakin's midi-chlorian count is more than that of Master Yoda.
OBI-WAN : Even Master Yoda doesn't have a midi-chlorian count that high!
... [later]
QUI-GON : A boy... his cells have the highest concentration of midi-chlorians I have seen in a life form. It is possible he was conceived by the midi-chlorians.
Star Wars Episode 1: The Phantom Menace
Yoda, after the birth of the twins suggests to split them up because of the very same reason. He thinks that the twins might attract much more attention together due to the affinity to the Force. And at the same time, if one is discovered, the other is still safe. As Obi-Wan Kenobi says,
YODA: Hidden, safe, the children must be kept.
OBI-WAN: We must take them somewhere the Sith will not sense their presence.
YODA: Hmm. Split up, they should be.
Star Wars Episode 3: Revenge of the Sith
As to why Leia (and not Luke) was taken to Alderaan, Senator Organa requests so.
BAIL ORGANA: My wife and I will take the girl. We've always talked of adopting a baby girl. She will be loved with us.
OBI-WAN: And what of the boy?
YODA: To Tatooine. To his family, send him.
OBI-WAN: I will take the child and watch over him.
Star Wars Episode 3: Revenge of the Sith