In the space between galaxies in the absence of matter, would time run faster than inside a galaxy? A black hole can slow time. Is there a cosmic opposite of that effect on time? Like the following question:
If time stood still at the event horizon of a black hole (wrt an inertial observer), is there a place where time would speed up in absence of mass (again, wrt an inertial observer)? If yes, What is the fastest time can get?
The space between galaxies isn't that much more empty than what we have here. There is some curvature, enough so that it causes gravitational lensing, even enough to make us suspect there's some extra matter (dark matter) we can't detect by other means.
What you're asking is directly measurable: it's the gravitational blueshift from whatever light sources you have between galaxies. It's not much... we're not that deep in the gravity well of our galaxy. Can't find numbers now, but should be pretty easy to compute, if you know the galaxy mass and your position in it.
