I could be a subjective matter. I would say Mt. Conness. It has all manner of good climbing routes, easily accessible and has some of the best views of the Yos. high country and the hi Sierra in general.
Matthes Crest. If you can solo a couple of pitches of 5.3 or so, then you have a mile of class 3 (in the photo) to the South Summit. Conness and Cathedral Peak are awesome, but not quite as awesome IMO.
One of the easier (class 1) hikes with spectacular views and no crowds is Clouds Rest from the Sunrise TH (near Tenaya Lake).
Also don't forget Mt. Clark, although it's a long, partly cross country hike, and to summit you have to climb a short very exposed class 4 section that feels more like class 5. Views are spectacular and chances are you won't see anybody else for a long time.
Gun to head (and given the class 3-4 parameter), I'd pick Lyell. It is remote, has a glacier, unbelievably beautiful, not very crowded and has a few Class 3-4 options. Can be done CTC in a day if you start very early and keep moving.
2nd choice would be Cathedral Peak via regular route. That Class 4 downclimb will get your attention
Conness is probably my favorite mountain in the park but I can't recommend its 3rd Class route, East Ridge as a fun outing. North or West Ridges are entirely different story
North Dome. We parked at Porcupine Creek trailhead on Hwy.120 ,hiked out to North Dome for the awesome views of Half Dome & Tenaya Canyon,hiked West on the North Rim trails to Yosemite Point and the Lost Arrow Tip to the top of Yosemite Falls.We only saw about six people before we got to the Falls,descended the Falls trail to the Valley, had lunch on the patio of the Ahwahnee ,and took YARTS back to Porcupine Creek well before dinner at the Tioga Pass Resort . We have also hiked down Yosemite Creek from Hwy.120 ,climbed Eagle Peak for the great views of Yosemite Falls and El Capitan ,descended to the Valley and returned on YARTS to Hwy.120. Have a great hike!