Some factors might be:
Proximity to the equator. The closer the launch site to the equator, the easier it is to launch to equatorial orbit, and the more help you get from Earth's rotation for a prograde orbit. Unless launching to a polar orbit, there's at least some benefit to launching from as close to the equator as you can get.
Downrange safety. You want to be sure that spent stages dropped along the launch path or failed launches don't fall on people or property. Eastern coasts are good for that, as long as you can exclude marine and air traffic along the launch path.
Every launcher in the world, except for polar orbits, launches to the east to take advantage of the rotation of the Earth. That is except Israel's Shavit, which launches to the west (Overflying its eastern neighbours looks like an attack).
Thus an eastern coast is a good choice, with lots of ocean downrange for dropping stages.
For polar/sun synchronous orbits a mostly northern direction, which in the US is usually from Vandenberg AFB in California.
The Russian sites use large expanses of desert to simulate downrange ocean.
Launch site safety/security. There needs to be an exclusion zone of some size (depending on the size of your vehicle) in all directions around your launch site to keep unauthorized people away from your launch facility, and keep things/people out of harm's way if the vehicle has a catastrophic failure at or close to the launch pad. Even if all goes well, exhaust from a big rocket can do serious damage to things on the ground from just the acoustic energy (shock waves, vibration).
Proximity to transportation infrastructure. Your launch site needs to be well clear of anything a failed launch can damage, but still close enough to roads/rails/docks to be able to bring people and material to or from it in support of launch activities.