If you click on the planet button when you are in the travel pane you will see the planet terrain layouts including where the cities are. You will just need to look for a city with a slightly different icon -
If you move the mouse over it you will see a tooltip which says NPC transport available. That is the city with the starport allowing you to move between planets.
Be warned however that the cost of transport is normally beyond the means of a starting player so you may prefer to join a faction and hopefully get them to pay for your journey to get to them.