Maybe call the White River RS in Bishop and inquire about snow conditions on the Paiute Pass trail. It is due west of Bishop, starts at ~9400' and tops out 5 miles later at ~11,500'. The views across a high, wide basin are beautiful, lots of jagged peaks to the west and south, with Mt Humphreys looming to your right(north-northeast). It's a pretty easy day hike, IF the snow is gone, and is about an hour and 20 minutes or so by car from Tioga Pass. Also,
a day hike from Lake Sabrina up toward Hungry Packer or Midnight Lakes would get you into some pretty spectacular country without topping out at a high pass and still fall in the 10-11 mile day hike category. It uses the same approach road as the Paiute Pass trail, but starts from Lake Sabrina. Snow conditions will definitely be the limiting factor, no matter where you go this time of year. Another possibility, if the road is open, is to drive up to Onion Valley and hike up to Kearsarge Pass. Again, snow conditions will determine your fate. Cottonwood Pass is probably the most likely to be snow free, but is a much longer drive and the views are not nearly as spectacular as farther north unless you want to hike on up toward Miter Basin, which is probably a bit longer than you want to go, from what you iindicated in your post. I hope you find something.