Any anons here experienced with camping and hiking in the national parks, late september and october?

I want to camp and hike in a few of the national parks, but i don't really want to book my sites a month+ in advance. I've found a few parks (yosemite and acadia) that are just completely full for august most of september already. some also close in early october.

can any anon here recommend me a good park to hike and camp (campgrounds, not wilderness), that i can realistically book about a week before i go there? somewhere where there's not gonna be snow in october and preferably good autumn colors. final requirement, i have to be able to get to the park without my own car.