Whale Trek?

I was lucky enough to meet a fellow geek today and long story short we were talking about whales and star trek, and he said that the Galaxy Class ships had whales or dolphins on board.

Can anyone shed some light on this?

Nope. Picard’s Enterprise never had whales on board—unless it was in some Trek novel that I’m unaware of.

Now, as everyone knows, Kirk did took a Klingon Bird of Prey back in time to 1986 in order to obtain some Humpback whales to bring forward in time in order to save the Earth.

What your friend may have been talking is the:
Cetacean labs

The Galaxy-class starship carried a complement of cetaceans. Among the crew, these facilities were also known as “the dolphin tanks” (TNG: “The Perfect Mate”) or the “aquatic lab.” (TNG: “Genesis”) In an alternate timeline, these facilities were also known as Cetacean Ops. (TNG: “Yesterday’s Enterprise”)

These labs are shown in the saucer section in the Star Trek: The Next Generation USS Enterprise NCC-1701-D Blueprints and are mentioned in the TNG Technical Manual. While the area itself was unfortunately never seen on the show, their existence has been confirmed in dialog. 

The blue prints can be seen here their are whale like outlines that can be seen:
Deck 13 - Shuttlebay 2 & 3
Deck 14

Well that is extremely interesting.
Why exactly would a starship be carrying a bunch of dolphins?
And if so, too bad they didnt have them when they were dealing with the Xindi. Maybe the dolphins could have talked to the aquatics.

Do you remember Seaquest DSV? They had a dolphin on board…

I remember being really young and sometimes seeing things about seaquest at like 3 in the afternoon on the weekends when they would show hercules and xena reruns.

Oh the joys of not having cable