Glad to hear you are going to stay in the Valley! Chick-on, Basilbop and I all agree best bet. ESPECIALLY since you have not seen it. We seem to never tire of the views!
My advice for any of walking/hiking during winter, carry traction devices like Kahtoola Microspikes.
At minimum, I would try to do The Eastern Valley Loop trail - Lower Yosemite Falls (definitely walk to the base of the falls) to Mirror Lake, (you should at least go to Mirror Lake and look up at Half Dome and beyond! There is an unpaved path around the lake if reasonable for snow conditions and your gear) and to Happy Isles (check out the islands), maybe walk to Lower Vernal Fall bridge, back around as far as you want. If you are doing this end of the loop and want more challenge - go up the Snow Creek Trail on the north side of the Mirror Lake loop trail above treeline for more views.
The views change as you walk around the Valley. There is the official undulating Valley Loop "trail" basically hugging the wall, but there are paved biking/walking paths (possibly under snow) that parallel and are not hilly, but offer different perspectives on the views of the valley walls.
Walk around the meadows on the boardwalks and paths. Look around! The free valley shuttle bus can ferry you around, if you want to jump around a bit.
There are so many little paths in the Valley, it can take days to wander them all if you are soaking in the views. In fact, Chick-on and I are finishing off little bits and pieces that he has somehow neglected over the years.
You can also walk the Valley Loop trail towards the western end of the Valley past El Capitan, over the Pohono Bridge, past Bridalveil Fall. Over Thanksgiving, Basilbop and I did that one day (about 11 miles) and the next day the eastern loop hitting Mirror and all... another 14 miles the way we did it.
If, after getting a good dose of the valley in a day, you really want a more vertical hike rather than wandering in the Valley, I'd suggest going up past the Lower Vernal Fall bridge up the JMT to Clark Point. If you want, continue on the winter route down to the top of Vernal Fall and up the side of Nevada Fall. But that's gonna take some time with snow.. and you only see a part of the valley, but it's gorgeous too. You really can't lose on views no matter what you do. It's a matter of preference as to what you'd rather see at any particular time.
Guess it depends on what elements of the Valley speak to you... Nothing wrong in my book spending two days walking all around the valley floor! Enjoy!
As for sequoia, there are younger trees in the Valley in various spots... but the really big groves of really big trees... well, the Mariposa Grove is off limits right now. Kings Canyon and Sequoia National Parks (both to the south) have the REALLY big groves of huge trees. Tuolumne Grove is nice and Merced Grove is cute. But both are along Highway 120 and need private transport, I think, unless YARTS is running by there.. but even then, with your schedule... come back some other time to visit the sequoia groves! And, IMO, they are WORTH visiting! (I'll be in Sequoia again President's Day, to do just that!)