We've stayed at a few of the Syracuse hotels other posters have mentioned, so for what it's worth, here are my observations...
Holiday Inn Express Airport is clean and fairly new. Really close to airport. But they have had issues with their park and fly situation (unpaved parking lot, vandalism).
Candlewood Suites Airport is a bit older but clean. Also close to airport. Rates similar to Holiday Inn Express, which is right next door.
Best Western Airport is an old motel in poor state of repair and not that clean. Would not recommend this one.
Holiday Inn Express Cicero is about 10 minutes north of airport just off HWY 81. New and clean. Decent place to stay.
Comfort Suites Cicero is close to the Holiday Inn Express. New and clean. Competitive rates. Would also be a good choice.
You might consider taking your car to the airport and leaving it in the parking building. Yes, it is $10 per day, but your vehicle is protected from the elements and waiting for you upon your return. That's what we have done. (You must arrrive early though, since the parking building fills up. Overflow lot is a bit cheaper but outdoors.)
Have a good trip.