Consider doing Mt. Whitney (14,462 feet) or Mt. Shasta (14,200 feet) instead. You *could* do day hikes, but it'd have to be a 17-18 hour day.
Whitney is actually quite easy since you start at 8000 feet and it's not that satisfying because the summit itself is only a peak along a ridge of mountains. No fun.
Shasta, on the other hand is a mother of a hike/climb. You start at 6,000 feet and you are trudging up this neverending hill for what seems like forever. Only 20% of people make it and someone manages to die each year, so it makes summitting VERY satisfying!
You can also do a combined wheeling/climbing trip on the NorthEast side, but that glacier is pretty challenging with lots of hidden crevasses and a very very steep ice headwall at the top. But it's definitely doable.
We did a two day'er and snowboarded down, making it much more relaxing. If you can handle the altitude, it's quite breathtaking. Otherwise, you'll be throwing up and passing out.