My university has single-user gender-neutral bathrooms in several buildings. They also serve as accessible stalls for people with mobility devices and/or caregivers in buildings that weren't previously up to ADA standards.
They are nicer, newer, and cleaner than most of the other bathrooms, and nicely private.
In addition, events put on by certain groups (usually LGBTQ student organizations) will take over existing multi-stall gendered restrooms and make them neutral, with special event signage. The signage also contains directions to the nearest gendered restrooms for those who may be uncomfortable with a shared space.
I really enjoy those, because people get the opportunity to realize that being in a stall next to a person of a different gender is approximately as awkward as being in a stall next to someone of a similar gender.