What is the relative velocity between planets in different solar systems? Is it possible to estimate what the difference in velocity is between the earth and another convenient exoplanet? Or perhaps just our star and a near neighbour?

I'd be curious where I could find the figures, and I'm wondering exactly what the magnitude of the difference is between relatively near neighbours.

Context:

Putting together an outline for a book, and I'm curious about something.

In the book, faster-than-light travel happens through instant travel between two points in space. In doing so, you retain all of your kinetic energy. This means you'll emerge at your destination with the same velocity as you had before you transitioned.

The bulk of the travel time in interstellar travel would simply be matching velocity with your destination before transition - the vast majority of the distance of the journey would be instantaneous, since for traffic control reasons ships are expected to come in at a reasonable speed when compared to their destination.
Tens of kilometres per second for nearby stars. Hundreds of km/s for stars in distant parts of the galaxy to thousands of km/s for stars in nearby galaxies. Anything from "much more" to "it's complicated" for stars in very distant galaxies.

The Earth is orbiting the sun at 30km/s and the orbital velocity of exoplanets is on the same order of magnitude. The stars are also moving relative to the sun. We can measure the transverse velocity for nearby stars by seeing them slowly change position (relative to the distant background stars) and we can measure the radial velocity by the blue- or red-shifting of the light. 

We can't directly measure the transverse velocity of distant stars, but their general motion is around the galaxy with a velocity, relative to the sun, in the 100s of km/s

Nearby galaxies are moving at similar velocities. Again, we can currently only measure the radial velocity, but their transverse velocities would be of the same order of magnitude, and in the 100s to 1000s of km/s.

Distant galaxies are part of the Hubble flow, and the expansion of space, so defining relative velocity or relative distance becomes tricky and needs to be done in the context of General Relativity, at which point things become more problematic, and beyond what is required for space opera.

For context, spacecraft in orbit around the Earth travel at less than 8 km/s and our fastest spacecraft (which are needed to travel close to the sun) have never reached 30km/s.