There are five planets that you can travel to using any kind of space ship:

Earth: Everyone starts here regardless of whom you are

4 days travel to Old Vegeta

5 days travel to New Vegeta

3 days travel to Namek

3 days travel to Yardrat

Old Vegeta: Mainly just a bunch of Asteroids floating around at a certain spot in space.

5 days travel to Earth

3 days travel to New Vegeta

3 days travel to Namek

4 days travel to Yardrat

New Vegeta: The planet where the Saiyans decided to make their new home planet

5 days travel to Earth

2 days travel to Old Vegeta

1 day travel to Namek

3 days travel to Yardrat

Namek: The native Planet of the Nameccians

3 days travel to Earth

1 day travel to New Vegeta

2 days travel to Old Vegeta

4 day travel to Yardrat

Yardrat: The planet where Goku landed after he escaped Namek

1 day travel to Earth, New Vegeta, and Namek

2 days travel to Old Vegeta