Speculative is the key word and pretty much defines the OP..
If we are visiting black holes, I would suggest we would be getting a boatload of energy ( with a lot to to spare ) from somewhere..
Okay, how about this:
My civilization has developed a Grand Unified Theory and unlocked the secrets of the Alcubierre drive. However, manufacturing the fuel requires stupendous amounts of energy. Over thousands of years, my civilization painstakingly harvested enough energy from our home star to send two Alcubierre ships to the two nearest neighboring stars. Once there, each of these ships spent thousands of years harvesting enough energy to power two more ships for two more short hops. Slowly but surely, over the past one hundred thousand years, my civilization has been painstakingly leapfrogging a growing fleet of Alcubierre ships towards the supermassive black hole near the center of our galaxy.
Once we get there, though? Everything changes. The energy given off by the black hole's infalling accretion disk is
ridiculous. Like orders of magnitude more energy than we can get from any one star. Within a decade of arrival, each of our ships is able to harvest enough energy for several long-range hops. Our ability to rapidly build advanced equipment and infrastructure increases exponentially.
For the past hundred thousand years, all we did was make our way, step by slow step, to the center of our galaxy, harvesting a fraction of the energy put out by the stars along the way. In the next hundred thousand years, we will visit every corner of our galaxy, and tap every star in it.
What will we do with all that energy? Build stuff. Feed our growing population. Fight wars, probably. Create art and entertainment. Further explore the limits of the high-energy and small-scale physical regimes. At some point we'll set out for Andromeda - something that wouldn't really have been practical if we restricted ourselves to merely harvesting from stars.
After that? The Virgo supercluster and all the energy in it is our oyster. Then the Pisces–Cetus Supercluster Complex. Ultimately, we intend to pierce the empyrian, and travel to those regions of the universe that have been causally disconnected from ours by the expansion of space.
Nobody knows what we'll find there, which is the main reason we're going. Whatever it is, it will probably suck balls though. Because in the end, our reach always exceeds our grasp, and hubris ever begets nemesis.
