There are a lot of nice hikes on the west side, but they tend to have (much) longer approaches to get up to timberline and the summits than east side approaches.
Yosemite/Ansel Adams Wilderness: I really enjoyed a couple of days I spent around Madera Peak (a short hike in a pretty area) and Foerster Peak (also accessed off Beasore Road). From the valley, Mt. Clark and Starr King are both classic peaks. And in early spring, Grizzly Peak/Mt. Broderick are really fun options from the valley. The peaks off Tioga Road are also obvious options when it opens up: Tresidder, Unicorn, Cathedral, Tuolumne, Ragged, etc. are all worthwhile.
John Muir/Dinkey Wilderness: Finger Peak is a nice peak, but it's about twice as long RT as your 25mi cut-off. There are some short peaks around there: Three Sisters has nice views, and close by is Dogtooth (some short but enjoyable cl 3).
Sequoia/Kings Canyon: North Guard is the classic peak IMO, followed by Mt. Gardiner and Thunder Mtn. There are a bunch of other worthwhile peaks around there, too... State Peak, Mt. Harrington, etc. For shorter hikes, Mineral King is probably the best bet, since you have only a short approach to get up above treeline and to the peaks. (And for longer hikes, it's tough to beat Black Kaweah). As Rob mentioned, both Alta and Silliman are good, and accessible even with snow cover.
It takes somewhere between 4.5-5h to get to Cedar Grove, if I recall. Probably 5h to Mineral King. I don't think it's much more than 5-5.5h to get to Bishop, assuming no traffic. So the time savings may not be all that much, especially if you look at east side hikes around the Hoover or Ansel Adams Wilderness.