I used to leave them outside the train station for visitors to pick up, but since I'm trying to maintain perfect town status for 15 days and don't want stuff left lying around, I've just been selling them to Re-tail.
I collected them at first because they're kind of rare outside of the rainy season, but they were getting on my nerves in the end, so I just sell them haha ^^
I've been using the exhibit rooms to store them too. Does anyone know if Brewster will still store them for you in the cafe, like in City Folk? If not I'm just going to sell them because I've never particularly liked them.
I keep them all in one of my rooms. I don't know what I'm going to do when I need that room for proper furniture, because I want to have one of each gyroid, for not other reason that I just can't not collect them all.
I keep cool sounding ones and all the yellow, red, and green ones for my rooms. I tend to sell the rest, but I just can't cause I can't re-order them if I ever want them back. D: