So, the setup. For the purpose of this question, there's no difference between a wormhole, stargate or teleporter. They all do the same thing - move an object instantly over space.
Because I've been thinking about it, and there are some real interesting complications caused by conservation of energy, which would significantly effect the energy cost of use - and if you don't have an infinite energy source, that will hit the cost of use. Some examples I've thought of..
You would always teleport to either in atmosphere (for areobraking) or orbit. Even on the same planet, if you teleported from one side of the equator to the other you would still have a velocity equal to the rotation of the planet in the complete opposite direction. Read: SPLAT.
Factor in both planets rotational and orbital speeds and your best bet would always be to appear right at the start of an areobraking maneuver which captures and then de-orbits you in a loop or two.
But this would imply that there would be very few windows of travel where this lines up nicely at the same point. You could do it year round, if you didn't mind where you landed - which means that a "Star Port" wouldn't work very well. You'd end up with tourist windows at intervals, but I can't work out how frequently.
But moving between planets would be Stressful. And expensive in terms of travel pods. Worse, you've got Gravitational Potential Energy. Going from Earth to Mars will cost you the energy to move further away from the Sun (And the gravitational centre of the universe, but I'm fairly sure that over a few AUs that's going to be small). That energy cost is really non-trivial - so importing Mass is always going to be expensive. You can send a moonbase... but you'd be better off sending a small one and then the means to build a big one locally.
Worse, going inwards would generate energy. Probably instantly. If you could hold that energy, or use it to power an outwards move at the same time you would have a really weirdly different cost for moving inwards. But getting out would be hellishly expensive in energy. (Going to the surface of the sun generates small warhead levels of energy. Think 1-10KT, for meaningful trips)
I've not even tried the numbers for looking at an interstellar trip. Could we even match speeds well enough to not go zooming out the system and never achieve capture??
Anyway, I can have a stab at predicting what will be cheap and what would be expensive. What I'm having trouble with is... what impact will this have on people? Travel between worlds would be expensive. Which normally says "For the rich!". But travel back would be HARD. And they wouldn't have comforts there. Any sort of mass trade would be really hard and impractical I think...unless you traded up and down at the same time. But what would Pluto's colony have to trade? Would we end up dumping stuff at one end or the other, to help the numbers balance?
What does this do to the society? Who does this favour? Who does it harm? And if anyone wants to do more math for us, to give hard numbers - please do!!