Sticking mostly to the downtown area.
Francesca's on N. Salina St. near downtown. One of my current favs. Exceptional in every way. Its getting too cold for this, but eating on the patio is a joy.
The Evergreen Downtown on East Water St. Casual Bar & Grill. You might be taken aback because you order your food at a window which is then brought to your table, but it's a great place with good food and and a great atmosphere.
A Pizza Regionale Not in my top 10, but alot of my friends like it. Owned by the originator of the Dinosaur BBQ. Upscale pizza joint with a nice decor and good service.
Laci's Tapas Bar This is a little outside of downtown and in a semi sketchy area, but its well worth it if you enjoy tapas style restaurants. Great food and decor, excellent scotch selection.
The Mission I love this place. Its in an old church by the Civic Center. The menu is hard to discribe; Kind of a mediterranean mix. Moderately priced and casual and usually very enjoyable.
Kitty Hoynes I'm not a big fan of most armory square places, but Kitty Hoynes is an exception. Great irish pub food. Always busy on weekends.
Ale & Angus I'm including this one because of location as its downtown, but on the campus side. It's a casual bar and grill, but they do great steaks, burgers, fish & chips, grilled salmon, etc. If you run out of options, this will serve you well.
For those staying at the Hotel Syracuse (or just looking for a place)
Shaughnessys Irish Pub is a sports bar that will probably be filled with game-goers that day. Not at the top of the list, but it would do.
Hope this helps!