Ok, Iím going to venture my opinion, that with that big of a group you would be better off camping in Mammoth Lakes and ďcommutingĒ for an hour to do your climbing in the Meadows. First off there is a ton more camping inventory in Mammoth both at the Lakes and in town. Secondly, the town runs a free shuttle service which can get you around town, to and from the lakes etc. Lots of nice hiking there, out of the Lakes and down at Devilís Postpile area. Thirdly, this gives you the option to access to a big grocery store (Vons) and numerous restaurants.
Like Jim says, the TM campground sucks. Buggy smoky and noisy.
I always stay outside the park and drive in to climb. I Just get to the Tioga gate by 8 am to avoid the entrance line.
I appreciate the central location of Tuolumne and how that helps a diverse group have a center....that said, I also like Porcupine (closest inside the park option) as a first come first served spot. Low key area, sites towards the back are better..
Yosemite Creek is great with the water feature, also first come, but a long way to get to the Meadows, including the 4 plus mile long access road...White Wolf is fine too...
Though you drive a bit to get to Tuolumne from these spots, you also are not in the chaotic Tuolumne campground et.
Going to Tenaya Lake each afternoon for swimming and picnic is de rigeur no matter where you are camping! So many things to do, folks will have fun, if you only have one car, Tuolumne is the only good option though...
Thanks for all of the information but someone here must know the answer to the question of:
Right now all pre-7/15 campsites are "unavailable" on the reservations webpage. If the campground opens before 7/15 when do those campsites become available to reserve online?
I think you are better off going to the Yosemite NPS site to see when the cg is opening.
When the reservations do open, make a reservation around 7am.
As Donini said, Junction cg is a nice campground, but small. One good thing is that you are right next door to Tioga Pass Resort.
One other option is the campground at Saddlebag Lake.
You really need to let go of trying to reserve. Its always a mess. Showing up early (5 am) at the kiosk for a site has worked for all us regulars for decades. Its really the only way to be sure to get a site.
I mostly discovered the eastern Sierra region because of my inability to plan in advance and uncertainty of getting a spot in Tuolumne, not wanting to burn vacation time hanging out in line. I discovered dispersed camping in USFS and BLM lands, and formed lots of great memories because of it.
If you are organized and punctual, more power to you with the reservation system, and if you are willing to burn a half day of your vacay waiting for your lottery position then coming back a few hours later... you can get it that way too.