If you get up early for sunrise, you can hit just about anywhere and you should be by yourselves. Otherwise, avoid the really popular stuff. You might try some of the canyon hikes (avoid Boynton Canyon, Fay Canyon). H.S. Canyon is a nice short one and has very low traffic, or maybe Long Canyon which has the same TH. Solitude seems a little easier find back there, and they are of course farther away from town, so they're very peaceful. I've done sunset on a Friday night up on Sugarloaf and had it all to myself...you're right next to town but you might be more likely to have it alone compared to most other places...but I've only been there once so no guarantees. I think Mescal Mountain would also be a good option, it gets barely any traffic, but it is kind of close to the resorts and it could be noisy if there's construction, probably better at sunset...the route finding is confusing at first on Mescal, PM me if you want more info.
I'm standing alone on the cliffs of the world
No one ever tends to me
Sitting alone, covered in rays
Some things are so my mind can breath