Yes, fly into SMF. I encourage you to stay in Sacramento because your day will begin in Sacramento. You'll drive to the UC Davis Campus at around 11:30.
If you can, make reservations at the Courtyard Marriot in Sacramento (I think it's on 45th and Y street). Then the main hospital is within walking distance from the hotel.
As for a ride to and from the Davis campus, just tell Terri you don't have one. you can either ride with someone else or take a cab. It's only 17 miles away, so it will probably cost like 30 bucks to get there (kinda pricey). Anyway, you could rent a car too, which I recommend doing at the Airport. If you cant, then call Super Shuttle to pick you up (costs about 15 bucks). Good luck and call Terri in admissions if you need any help. They are more than kind.