I see that to spawn a CP ship, you need to be on a landing pad or a starport. Where can I find these?

You can find them where they've been built on planets. If you're on a homeworld, there should be a city on that planet that has a NPC-owned starport you can use (find this city by its unique image on the planet map).

Otherwise, we can't tell you OOC where to find IC entities.

NPC Starports can be found in all race homeworlds, and the city has a special icon marking it. Otherwise, you ask around.

Thanks