I can walk for quite a while on soft ground, or could until the wound issues, but it has been a while since I had to give up walking on asphalt in the neighborhood. It makes a huge difference for me. My doctor's reasoning with both the parking and the wheelchair is that I should save what energy I have for the event, not use it all up in the parking lot. I would encourage you to use the permit.
Standing kills me. Last time we went to the Baltimore aquarium, several years ago, one of the museum attendants asked me several times if I wanted one of their wheelchairs. I must have looked pathetic. Now I take my own. Last year I tried to do a small local art museum without it and it was really a mistake.
I think the level of disability really creeps up on you.