From places in Flagstaff, proper, you're less than 30 minutes from where the Ski Lift Lodge is, and from there it's maybe 10-15 minutes up the Snow Bowl Road to the trailhead, so it really isn't a big deal. The second time we were out there in 2008, we stayed in Flag because of the Konvention. Had to get up a half-hour earlier to be at the trailhead at first light, not a big deal. Altitude difference is minor between Flag and the base of the hill, too.
I do suggest getting a very early start on Humphreys. Starting at first light, we made it to the summit before any storms blew up but the clouds started to build while we were taking our summit photos and there was lightning behind us before we got back to the Humphreys/Agassiz saddle and the trail down into the forest. The weather changes quickly and when you're on the summit, you're a good mile away from the first available cover if t-storms pop up. Pretty typical of a lot of the "walk-up" western peaks. Wheeler (NM) and Elbert (CO) are pretty much the same...fairly long exposed ridges where you do not
want to be in a t-storm. Whitney (CA) is even worse...about 2 miles just to get back to Trail Crest and then you have the 97 switchbacks before you're down into the rocks around Trail Camp.
There is a webcam
pointed at Humphreys from somewhere around Flag. You can't actually see Humphreys...Agassiz is closer and hides the taller peak, but if you watch the weather pattern on the web cam for a few days before your planned climb, you can get an idea of what time the storms start to blow up before you head up the hill.