So you managed to build a stable traversable wormhole. Somehow you managed to acquire the exotic negative-tension materials with sufficient densities to make it all work.
Now you place opening A of the wormhole deep inside a gravitational well, and the other opening B far outside that well.
What would a traveler approaching wormhole A experience?
A traveler that is stationary in regards to point A would have to expend a considerable amount of energy to reach excape velocity, leave the gravity well and reach point B trough normal space.
Conservation of energy implies that they would need the same minimum amount when going through the wormhole.
The distance they travel however is much shorter, and I cannot see how the required escape velocity can be the same. Do they therefore experience a stronger gravitational gradient along their journey?
Are they perhaps strongly repelled from opening A and for that reason have to expend the same amount of energy they would need to move out of the gravity well in a normal manner?
In the same vein, is a traveler approaching wormhole B strongly attracted towards it, so that they can gain the same amount of kinetic energy that they would get when traveling towards the gravity well in free fall from B to A trough normal space?
How does the spacetime around the two wormhole openings in different gravitational depths look like?
The wormhole itself will of course have a considerable mass of its own, and the exotic matter used to stabilize it will have its own weird gravitational effects, but let's assume that those are negligible compared to the effects of the giant gravity well that is near one of the wormhole openings.