One more question. I thought we had decided on Tenaya Lodge to spend a couple nights after Yosemite Valley Lodge for 4 nights. But then I started looking at Double Eagle Lodge in June Lake. It seems to have a lot of nice hikes nearby. Can the same be said of Tenaya Lodge? Obviously June Lake would be further to return to Fresno Airport (4 1/2 hours). Any thoughts? We have not been to this area, so I feel like I am being very indecisive! Thanks again for your recommendations!
I haven't stayed at either one. However, to me Tenaya Lodge seems to be too close to Yosemite to give you much of a different area, but too far to do a lot of different things in 3 nights. June Lake, on the other side of the Sierras, at least is near high country. There's a lot of hiking and fishing out there, Mono Lake and Devil's Postpile NM aren't far, and of course the drive over Tioga Rd is just gorgeous.
Not only is it longer to the airport, but the terrain is entirely different. You were asking about hikes. Why would you be spending time hiking in *either* June Lake or near Tenaya Lodge if you could go hike in Yosemite? I mean seriously, there's a reason Yosemite is a national park. Right now, June Lake is fairly unimpressive to me (and yet, Yosemite is a gem, a green, growing gem).
Tenaya is much nearer to Yosemite. You can walk out of the hotel and while there are no trails, it's beautiful evergreens. I don't know what property you're looking at, at June Lake, but if your goal is to hike around a lovely Sierra Lake (and not see Yosemite) then go to June Lake. Or, add another night to June Lake.
Driving over the Tioga pass each time you wish to see something in Yosemite (such as Vernal Falls or Glacier Point) is not what I would recommend. Still, having already spent a great deal of time in Yosemite, I can imagine just staying put at June Lake (like nearly every one else).
If you don't mind the drive, yes, June Lake is lovely. But it is its own destination (as JenAzz suggests). Just hang out there, don't be planning a daily commute to Yosemite Valley. If you want to spend time in a lovely (not Yosemite) place, then June Lake is great. Tenaya Lodge is also in a great area, but you will feel like leaving each day (and driving the 1.5 hours to Yosemite Valley).
June Lake is a destination all by itself and I predict you won't want to keep driving over Tioga and through the woods to Yosemite Valley.
But if you had 4 nights in the Valley and 3 nights in June Lake and you decided you wanted to do hikes or see more of Yosemite's high country, you could still go back in the park (your pass is still good by the way). Double Eagle is a destination in its own right, unlike Tenaya.
A lot of this depends on how much hiking you want to do in Yosemite, whether you want to do high country hiking in Yosemite. Since you're going in September, you might appreciate the cooler temperatures at June Lake afterwards (if you truly are just going to relax in one place).
It all depends on the overall plan for your trip! You'll have had 3 full days in Yosemite which sounds like it's a lot, but many people find that they don't get around to doing all the things they wanted to do. The day you leave, you may want to plan some hikes around Tuolumne (or one from near Lake Tenaya, which is nowhere near Tenaya Lodge, ha - it gets confusing).
That way you'd have had 4 days in Yosemite and probably would be ready to relax for 2 more at June Lake.