Hi paxto13!
Welcome to the forum.
Several of us, Basilbop, Chick-on, mrcondron and I have discussed recent requests like yours about backpacking as their first experience with Yosemite.
We have all backpacked in Yosemite extensively. And by extensively, every freaking mile in the park except 1 maybe, in Chicken and Mike's case. Basilbop and I have been hiking and backpacking there for over 20 years. I was 3 months old on my first camping trip there, and have been going every year of my life since.
And we've all traveled to see other parks, other places.
And we agree. If you've never seen the park, ignore the people and the crowds (or feel good that they are there to see Yosemite instead of watching TV at home, as I do) and do the tourist thing and see the Valley.
My suggestions:
- Take a day or two to see the sights from the Valley. Walk to Mirror Lake and look up at Half Dome.
- Definitely visit Glacier Point somehow to get a better sense of the Valley and beyond. Drive/bus up or take a day to hike up the Four Mile Trail and either take the bus back down, or hike back down, or go over the Panorama Trail and down the Mist or JMT to soak up the views of the Valley and the high country from Glacier Point.
- Take a day to drive up to Tuolumne Meadows. Definitely stop and walk out to Olmstead Point if the weather is decent. The views from the parking lot are fabulous, the short walk even more so. VERY rewarding. One of the best views of Clouds Rest you can get with a short walk. See Tenaya Lake. Take a swim. Go to Tuolumne Meadows and see the high meadows. Take an hour (or less maybe if you are short on time) and walk up Pothole Dome for better views of the surrounding peaks. Drive to Tioga Pass and maybe beyond a bit to soak in the views of the fabulous canyon.
- If you've never seen the Giant Sequoias... Visit Tuolumne Grove (other years we'd point to Mariposa Grove, but that's closed right now for work). And Tuolumne Grove is lovely, in and of itself.
Sadly, in September, the waterfalls won't be spectacular, but the granite walls of the Valley are worth seeing from below and above.
In September, hopefully you can grab FCFS campsites around the park to make the driving and touring about easier.
The hardest hike on the list above is the Four Mile Trail up to Glacier Point and over the Panorama Trail. I suggest because if you have trouble, you can maybe take the hiker's bus back down, or hitch a ride. Or have someone stage a car up there... options.
You said Intermediate hiking ability, which I really don't know how to interpret. Unless you can tell me how you do on a trail I know, I can't extrapolate and figure out what trails would be good for you. Yosemite trails are well-used and often in rough condition. Where you hike may not really be an indication of how you'll do in Yosemite. Altitude is also an issue. Are you good at 10k'? (Clouds Rest, for instance.) Driving up to Tuolumne Meadows and hiking up Pothole (easy) or Lembert (much harder) Domes is a good litmus test. You may want to start easy and spend a couple days down in the Valley enjoying the views and short walks to Happy Isles, over to Mirror Lake. Maybe going up the Snow Creek switchbacks a bit for views into Tenaya Canyon. Get acclimated. Then either hike or drive up to Glacier Point at 7200'... see how you do there. If you drove out, maybe take the walk to the top of Sentinel Dome. See how that goes. Then go for Tuolumne Meadows at closer to 9000' and do one of the dome walks to see how you are doing... before you attempt the shortest way to Clouds, which is still 14-ish miles and can feel longer, especially with the 1000' climb to the saddle from Sunrise trailhead. And most folks underestimate how much fun dropping 1000' in short order at the end of a 14 mile day can be. I've heard of many who have hurt themselves.
Take the time to see the views from the "touristy" areas. We still visit them every year. Often, several times a year. Granted, we have the luxury of visiting some the busy places off-season, so it's quieter. But I still love going peak season for the views. And I'm happy to see people enjoying Yosemite. Get the overview of the park. Decide what you really want to see... because backpacking will give you an intimate knowledge of the area you are hiking in, but in 5 days of backpacking, you just won't get the overall sense. Yosemite is huge. No way to capture it all in 5 days.
And again. The Valley is not to be missed.
And I didn't even mention the other Valley. Hetch Hetchy, which is worth a visit in and of itself. But will eat a day of traveling, especially if you hike the 6 miles round trip to Wapama falls and back, which is worth doing, imo.
Sorry this wasn't edited as well as I'd like, but I had to say something... I wish you a fabulous trip to Yosemite no matter what you choose to do!!