currently utd but prior to that I kept my sanitary items in a bathroom drawer. that way I could pop something in right after a shower. our upstairs toilet is separate from the bathroom but if I was just using the toilet and needed a change of tampon/pad, I'll just go to the bathroom (also upstairs) and do it there then wash my hands after on the way out.
our bathroom kind if adjoins our bedroom (one of those stupid semi en suite but not really type things) so if I had to, I guess I could keep sanitary items in our closet. more convenient in the bathroom though.
we have a powder room downstairs but that's just a loo and little hand washing station in the one tiny room and I keep it really just got guest use. so I don't keep any personal/sanitary products in there at all.
it's a bit tough with one bathroom I agree.