Good Day Hikes From Whitney to Yosemite

This certainly does not meet your mileage, but Mount Dana is always fun. It is about three miles southeast of the Tioga Pass Entrance Station for Yosemite, and its summit is slightly over 13,000'. It used to be 13,053', but with tectonic movement, it may be up a few feet from there. Strong hikers can go up in two hours, but most hikers want to take three or more for the uphill.

–B.G.–

is this for before or after the JMT ?

The Palisades out of Big Pine,
South or North fork of Big Pine Creek.
my preference would be North Fork, up to 3rd Lake and back, about 10 miles round trip I think.

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All of the major east side THs provide excellent 10-15 mile day hikes:

Horseshoe Meadow – summit Langley
Onion Valley – you could hike to where you crossed the PCT a few days earlier
Big Pine – doesn't cross the Sierra crest (unless you like class 3 Jigsaw)
Bishop Pass – same as OV – a little further to the PCT, but doable
Piute Pass – lots of lakes before/after the pass
Rock Creek – really popular – same idea as Piute – could go over Mono pass
Silver Lake – same as OV – hike to where you crossed on the PCT
Gaylor/20 Lake – mess around with part of the SHR

The day hikes would be after finishing the JMT.