The space under the kitchen cabinets is dead space used for heating and plumbing, but there is still a decent amount of usable space left under there. So I unscrewed the access panels and added some strips of magnetic tape on the cabinet side, and some strong little button magnets on the removed panels. For a way to open them I just used Gorilla Tape (my favorite stuff!) and taped a little ribbon pull on the top of each one.
I would have liked to add matching doors or something, but this will do for less frequently accessed stuff and is most certainly more cost-effective :).