Motioning to her newly-minted accreditation and saying she'll "see [Kirk] around the galaxy" doesn't make much sense to me if she's just talking about doing her "three hundred years of catch-up learning" on a boat in the Pacific.
It was a figure of speech. It didn't have to make sense. Also I think it was a polite brushoff. Gillian never really responded to Kirk's charms, so she was basically saying goodbye and had no particular intention of "seeing" him anywhere.
Yes, she could be on a ship on Earth but if some months did take place at the end of Star Trek IV perhaps she is "assigned" to a vessel which does ocean research on many worlds, not just Earth.
But that doesn't make any sense. The whole point of the mission was to bring the extinct humpback whale species back to life. You can't just bring two specimens back from the past, dump them in an ocean that's been devoid of their kind for centuries, leave them to their own devices, and hope for the best -- they'd be dead in weeks, months at the outside. If George, Gracie, and their offspring were to survive, if the species were to be repopulated, it would be imperative to monitor them for the rest of their lives, to develop a breeding program, to figure out what they needed to eat, to protect them from 23rd-century disease organisms, etc. And Gillian Taylor is the only person in the entire Federation with direct, firsthand experience with the biology, behavior, and environmental needs of living humpback whales. Nobody else could do the job. She has to stay with the whales. Anything else would be criminally negligent. Anything else would doom the species to a second extinction.
Besides, why would she want to leave George and Gracie? She was so attached to them that she abandoned her entire life and travelled three centuries into the future to be with them. Do you seriously think that after that, she'd just casually walk away from them? Of course not!
Kirk inquires how he will find her, she responds "I'll find you". Well, she won't find him on Earth. His job is in space. This dialogue certainly can lead many fans to believe she will be spending some time in space.
Or that she would be capable of using a subspace transceiver and "finding" him the same way you find someone's number in the phone book and give them a call. Or that she was politely brushing off this flirtatious older man that she had no interest in.