From Three Rivers, I would stop first at Hospital Rock. Park and walk across the street to see the petroglyphs and learn about the Native American history of the area. Then I would head to the Giant Forest Museum. Then on to Tunnel Rock for a photo op, then the Moro Rock stair climb, and then off to explore Crescent Meadow. There I would go to Tharp's Log and Chimney Rock. If you have time, hike up to Eagle View, especially if it's a clear day. After that you could head to the General Sherman tree and hike the Congress Trail, a really cool hike with so many big trees.
The next day you could drive straight to the Grant Grove entrance of the park, taking Hwy 245. Drive down the canyon to see Grizzly and Roaring River Falls and Zumwalt Meadow. On the way back stop at Grant Grove, which is every bit as impressive as General Sherman, if not more so.
If you have more time on another day, the hike to Topokah Falls is really nice. It starts at Lodgepole Campground. If you're not staying in the park because of cost, I understand. But, if you're not staying there because you can't get a reservation, keep checking for cancellations. Staying in Three Rivers will be a lot of driving no matter how you plan your day.
It's a beautiful park and I hope you enjoy your time there.