If you're staying near the hospital it's a pretty easy walk to the game. For what it's worth, I've walked from downtown to the University, or vice versa, multiple times over the years and it's not a bad nor unsafe walk, and the walk to the arena is far shorter. The easiest route from the hospital is up the Corner (University Avenue where all the shops and restaurants are) to Rugby Road, across Beta Bridge (obvious from the paint all over it), immediate left turn, go past the Lambeth Colonnades, then follow the path down the hill and over the pedestrian bridge.
Driving all the way down on Friday afternoon means the traffic will be a crapshoot, as froggie mentions. At 2:00 PM you'll be too early to take advantage of HOV on I-66 westbound. It's hard to say how traffic will be on there or on I-95. I wouldn't be surprised if there's some volume of long-distance traffic due to people making an early getaway in advance of Christmas, but then since Christmas itself isn't for another week it won't be horrible and I'd expect you'd encounter more mall traffic than long-distance traffic. If you have an E-ZPass, the I-95 HO/T lanes would likely provide you with more of an "express" trip than the left-lane HOV-2 facility outside the Beltway on I-66–but then again, the HO/T lanes do back up at their southern end, so you'd want to be ready to bail out at Quantico (the BGS in the express lanes lists Route 619).
If you do take I-66, you have three good options for connecting to Route 29 south to Charlottesville:
(a) Take Exit 43 for US-29 at Gainesville. Easiest route. Some roadwork still going on in Gainesville but the biggest part of the work is done. There are a bunch of annoying new traffic lights between I-66 and US-15 associated with commercial sprawl.
(b) Take Exit 40 for US-15 at Haymarket, go left at the light, then follow to US-29 and turn right. Note this is a two-lane road with an at-grade railroad crossing and it is definitely no longer an "undiscovered" shortcut. I-66 is also being widened between Exits 43 and 40, so there's construction to deal with.
(c) Continue further west on I-66 to the next exit after Haymarket for VA-245, marked for The Plains. Go left at the bottom of the ramp and follow it a mile or two to US-17, then go left again and follow it to the Warrenton bypass. It'll put you onto US-29 just east of Warrenton and just west of another short commercial stretch. This route is longer mileage-wise. It can save time depending on the time of day and the traffic volume through the Gainesville area.
BTW, if you want a great dinner spot for Friday night, I love the Shebeen South African pub in downtown Charlottesville. It's located off Ridge-McIntire Road in the Vinegar Hill Shopping Center, a tiny strip mall across the street from the Omni Hotel next to McDonald's. I think I've liked everything I've had there. It's off the beaten track in terms of places the students frequent, which means it tends to be less crowded. If you like sitting at the bar and watching rugby or soccer on the TV, this is definitely the place to go, but of course they have regular tables as well. The mussel appetizer is outstanding.