I wonder if I should just turn this into a road trip, beginning and ending in Reno? The weather looks bad from a Southerner's perspective. Hmmm.... NorCal, or flee south, or....?
Well, it looks like you basically have three days you could road trip. Depending on how much driving you like to do in a day, a couple of trips might be:
1) Head down 395 to the points I mentioned. You could additionally go farther south and hit Death Valley for half a day or so. Overnighting in Bishop, Lone Pine, or Independence would probably be your best bets for that. You're looking at maybe ~250 miles to Death Valley, so maybe 600-700 miles total if you do the whole thing. It's a big park, so you wouldn't be able to see all of it, but you could definitely make the tourist attractions. If you don't want to travel that far, Mammoth is fun even if you don't do winter sports. Check VRBO for condo rentals that will be cheaper than any of the hotels, and often much nicer. Or you could splurge on a place like the Tamarack lodge and get a cabin by the lake and fine dining for a night.
2) Head West to California and maybe try turning North and doing highway 1 for the killer coastal highway/redwood trip. You could potentially veer into Oregon and stay in Ashland overnight, then head back to Reno via I-5/hwy395 (if open) or I-5/I-80. This is a much longer trip though, 1000-1500 miles depending on how far you go, so you're on the road most of the time. Also note that we're getting heavy rains in CA for the next week, and that often shuts down parts of HWY 1.
3) Just hang out around Reno /Tahoe/Virginia City and relax. :)
I left out heading East because there's pretty much nothing between Reno and Salt Lake City.
What was said earlier about chains still applies. Note that it doesn't mean you'll be putting them on, but the chain restrictions require you to show the cops that you have chains with you. It seems like once full restrictions go into force, they usually shut the road down anyway, so the chains are just to check the box. There are chain restriction zones along 395, 80, and 5, so any road trip you take, you're gonna run into a restriction zone (which again, may or may not be active). There should be plenty of places in the Reno / Tahoe area that will rent you chains at a reasonable cost. Heck, the car rental place there might even do it.