You may only go to another planet if you have a space ship, otherwise you must stay on Earth. training may be more intense on other planets, or there could be Sagas that you must do on the page.

Saiyan Planet Vegeta-
This is a small planet, once home to all the full blooded saiyans in the universe. Unfortunatly, to this day no one currently survives on this planet. On this planet you may do harder training, the planet has gravity twice as good as earth (=to a gravitron with a x2 upgrade). It takes 5 days to get to Vegeta from Earth so bring a friend along. On Vegeta, no one is around, so there are no items to buy.

Namekian Planet Namek-
This is a large planet where Kami came from. You must go to this planet after the saiyan saga to wish back your friends lost in the battle with Nappa and Vegeta. There is so special Training upgrade on this planet, but you must do the Frisa saga here. It takes 5 days to get to Namek from Earth.

King Kais Planet-
Here you recive training from the North Kai himself and his sidekicks Gregory and Bubbles. This training does wonders for you though, you must be dead to get there. It takes 1 day to get there from any planet.