In my old (1981) bathroom vanity, that I just removed, the air came up from the floor into the enclosed space under the vanity, then out a vent in the toe kick (no duct), it worked great.
But my problem is different now. The vanity I bought has short legs -- no toe kick, no enclosed space underneath. The clearance from the floor to the bottom of the vanity is just 2 1/2". The HVAC duct (6") comes up from the crawl space through the floor, 4" in from the wall.
I could install a floor vent under the vanity, and air would, more or less, find it's way to the room. But mostly, wouldn't I be making the vanity itself nice and warm/cool? I'm not very concerned about the air hurting the solid wood vanity (like from expansion/contraction, and I don’t see how a vent underneath would be much different for the vanity than air going into enclosed space under a vanity) -- my concern is how inefficient it would be for heating and cooling the room.
But I don't know what else to do (short of moving ductwork in the crawl space to a location not under the vanity; it's a tiny bathroom and a horribly cramped crawl space, I'm really not up for that) -- any suggestions?
Thanks very much! ... Rick