And here’s me about two hours away from my copy of the Star Trek: The Next Generation Technical Manual to debunk this obvious joke with a picture of all the architectural diagrams where it calls out places where one might find a head, including, IIRC, the Ready Room, of which I imagine Riker probably avails himself on the regular.
I mean, they have a transporter right? Couldn't they just beam waste into a holding container or out into space? In discovery they say they recycle everything so maybe it just gets beamed to Kieko's Arboretum lol.
The whole idea of Replicators and Transporters is that they have some technology which can efficiently convert matter and energy, so it's possible that they use some sort of reverse-replicator to process waste.
You also never see what they do with the glass cups the replicators create when someone asks for a drink...
By the 32nd Century, it is confirmed canon that human waste is directly reused for food replicators. "It's pretty good for shit." - Admiral Vance
It's less clear whether that's true for earlier eras or not, but the existence of "matter recyclers" sure implies it.
But all this still doesn't address the matter of where people poop on a starship.
Surely the bridge crew all have their own freshers, but what about the lower decks? Do they have communal restrooms? What about accomodations for different species needs? Is there a diplomatic lounge with a wide variety of bathrooms available? When they have guests from a different species they're not familiar with, is there an ensign whose job it is to research that culture's bathroom customs and ensure they have the appropriate facilities replicated and constructed? Is there maybe a small holodeck reserved for this purpose? These questions need answers.
The head was visible in a few episodes, but while the doorway was initially labeled "CONFERENCE" in "Gambit, Part II", it was relabelled "HEAD" by "Emergence". In addition, in episodes throughout the seventh season, multiple crew members can be seen simultaneously entering the bridge via the head. It is unclear how many toilets are available for use in the head on the main bridge.