I've done a trip almost every year since 2007, and a few before then but not as regular. I've been to most national parks out west and a few lesser known in Oregon/Washington.
Typically we go 5-7 days and average 7-10 miles/day. Never had a guide. I'm also fat, so you should have no problems if you can run 6 miles. I can't run 1. Ok now that the intro is done...
All parks are slammed this year, so will be tough to get a permit. Glacier starts taking permit requests mid-March and and 2-3x their usual requests. I don't know how Yosemite works.
Given this info - I fully agree w/ the other posters that later September will be the only way to go this year, will be tough before then. You may see snow in October in some places so just beware.
I love Glacier - it's my favorite park. The "North Loop" is on my bucket list, it's about 5-7 days. I've been on parts of it and it's the best stuff I've seen, but other stuff does come close. Any hike in Glacier will be better than Yosemite.
My opinion, the views at Yosemite are good but not nearly as good as Glacier. It's more "rolling" mountains as opposed to "peaks" (there are exceptions, but generally Glacier has more peaks, like the Alps).
I REALLY want to do the Tetons but their permits for the 4-day loop fill up in about 5 minutes when they are issued in January. Now I wonder if guides are snagging them all? But that would be better than Yosemite.
Both Tetons and Glacier save half their backcountry sites for walk-up only. So if you go late September, you may have luck getting a good trip. It's a bit of a pain, you need to be there by 7am (or earlier in the summer) but it's an option.
The Sawtooth Mtn area looks nice - thank JoeLee for sharing that. We are looking for a trip as well in September, so may look more into that.
Other ideas - PM me if you want more info, as I don't have time to find links for all these right now, but you can see if any sound fun and I'm happy to share info, as this is my favorite thing to do in life...
4-pass loop outside of Aspen Colorado : No permits required last time I checked, loop is 26 miles or so, so you can do in 3 days but I'd recommend 4, since being outside longer is usually my goal.
Eagle Cap/Wallowas in Eastern Oregon : No permits, not many people know about it, but search for "Eagle Cap Oregon" , it's just beautiful, also better views than Yosemite
Rae Lakes, Kings Canyon : The John Muir Trail starts in Yosemite and ends at Mt Whitney, and passes thru Rae Lakes. Really good scenery here and the lakes are unreal. Also good access if you fly to Vegas and drive thru Death Valley.
Spider Gap/Buck Creek Pass, Washington : No permits. My first 6 day hike, would love to do again. You hike up 1-2 miles over a snowpack on the 2nd day, views are incredible the whole time.
Rocky Mtn Natl Park Loop from Grand lake to Estes Park and back : Really great, good wildlife, I think 34 miles with a side-trip, or 28 without. Not sure how the wildfires affected this area though.
Good Luck!