Chiming in a little late here, but I did this last summer (July 2019). And things to do in King Salmon are....limited. The town itself includes 2 restaurants (really bars), 1 convenience/grocery store, and a couple of small cottage-for-rent type motels. All within about a 5 minute walk of the airport. If you go out a little farther, there are bigger, pricier lodges that focus on fishing--we stayed at the King Salmon Lodge, which provided pickup/dropoff at the airport. Lodging was fine, food was fine, but it's really a fishing lodge, and not cheap. There are others in the area, and I'm sure they all offer pickup/dropoff because there are limited rental car options in the area.

There ARE taxis, which are accustomed to people doing what you're doing--spending the extra day in King Salmon to be on the safe side. We did it. Naknek is a $15-20/person cab ride away; another small town with 2-3 more restaurant/bars and some commercial fisheries. We walked out to the end of the peninsula past a few canneries. At a slow pace, it took maybe an hour. Got lunch. Called the cab and went back to the airport. Spent the next 4 hours in an airport the size of a large SUV. (Actually, the National Park Service office adjacent to the airport is not bad, and the gift shop at the airport is surprisingly pretty good.).

We ran into a couple on our trip back from Brooks to King Salmon who didn't have a reservation, and couldn't find a room. They had camping gear, and the folks at Katmai Air were going to let them camp on their property if necessary so they'd have access to a port-a-potty. So there's always that as an option

Seriously, I'd plan on finding some good hikes and/or fishing. You're going to one of the coolest places in the world at Brooks Falls; we were only there for 2 days so didn't do the Valley of 10000 Smokes, but talked to one couple who enjoyed it. Take the best camera you've got, go out to the platforms at the falls as many times as possible during as many different times of day as possible, and enjoy the trip!!!!