Yeah, Trailhead 19 (Sunrise) is the one to use. It's packed solid on reservations for Sept, and that's not a good thing. Middle Sunrise Lake is your best bet for privacy, but that route is crowded, crowded, crowded, so it's not likely you'll have maybe as much as you might want. This is the correct site for checking out what trailhead reservations are full:
https://www.nps.gov/yose/planyourvisit/ ... lheads.pdfWith a "daily" permit, it's actually going to be called a walk-up. Walk-ups constitute 40% of daily trailhead quotas. Strategically, you have two choices: get to the permitting station early for the same day, or after 11am for the next day. I don't really recommend one over the other. It's timing and what others are thinking. If you do end up with a permit for the next day, you can stay for $6 apiece at one of the backpacker's campgrounds at Tuolumne Meadows, White Wolf, or even at the North Pines campground down in the Valley. The best alternate entry trailhead is 17 (May Lake). You only add a couple miles, but you then have to hike back up or hitchhike to return to the car...no shuttle.
Okay, so here's Plans B and C. It's hard to compete with Cloud's Rest, but here are a couple alternatives with huge views and incredible, romantic, often private campsites.
The first is the one Transponder suggested, the Snow Creek overlook. It's one of my personal favorites. Entry is Porcupine Creek trailhead. Easy 4.1 mile trail. All downhill. You can exit in the Valley at Mirror Lake and shuttle back to the car, or you can hike back out on the same route. Another alternative from the same trailhead would be North Dome. Camping there, as well as spectacular views.
Next would be the trail out of White Wolf down to Pate Valley. Camping with incredible views overlooking almost the entire length of Hetch Hetchy is about 5-6 miles out from the campground, again all downhill (until you have to get back) and on some nice fairly roomy ledges tucked into the side of the cliff to the left of the trail at the top of Morrison Creek. This is probably the best of the three possible routes for finding a private site, and the views are huge and profound. You're also not going to have any problems whatsoever in getting either a reserved or a walk-up permit. It might seem like an outlier to what you had in mind, but it is by no means any sort of compromise. As a beginner, you'll not only have an easier time of it, she'll melt into your arms and know for certain that you're the one by the time you have the tent pitched. And this is not only a theory.
As a matter of fact, since you are a beginner, I would probably take Plans B and C over Cloud's Rest. I could look back on my relationships over the years and confidently tell you that if I took 8-9 out of any 10 women that I've ever been with up to CR for their first backpacking trip, they would've hated my guts long before we even got back to the car.