I went to YNP right after Labor Day several years ago. I've been there maybe 20 times. I was surprised at the large number of people -- even at that time of year. You can't beat YNP for seeing wildlife and geysers, but other than that I'd agree with the others that a wilderness or semi-wilderness trip would be more fun.
Although you CAN (legally) carry firearms in the Park, that doesn't mean you won't get dirty looks and maybe snide comments if anyone sees them. Bear spray is encouraged. Be sure you get a copy of the backcountry camping regs BEFORE you leave home. Food storage is one area you'll want to be familiar with. The bear-proof containers wouldn't hold a decent lunch; let alone several days food --- okay I'm exaggerating a bit.
Weather might be in the 20s 30s 40s 50s or warmer/colder than that. We got snowed on twice; once heavily.
who cares if you get "dirty looks"? those that do care are sheep IMO...
thats the problem with our society these days... worrying about what other people think... well i can tell you, us folks from/in montana could care...less...!

its just the tourist that care... and if they do, they should go back to suburbia to their little castles or asia and stay there, while we life free...

just my 2 cents...