AirBnB does not really want you to search for anything other than the city or region you're staying in. It's all map-based once you select your region.
And most travellers do not wish to reveal too much about their visit when they're travelling, not that they're hiding something, but because they don't necessarily want to be discounted by the host. Say, if they're coming for a concert, they'll say "a weekend visit." I would imagine that if they're coming for a hospital visit they are unlikely to want to get into the specifics with the host.
Ensuring you're only renting to family members of patients at the Jubilee is going to be very tough, unless you state in your description that the rental is purely for individuals seeking proximity to the hospital. But then, what would stop someone from claiming they are especially with your low-low-low rate of $80/night for a full suite?
I think you're doing a great thing, but because you can't get onto a list handed out by the hospital, you can't market ONLY to your intended target.