Cebu is a pretty cosmopolitan place and alot to do as far as nightlife and dining. The view from Tops is always recommended and a bit romantic. You can get a meal up there and look at the city at night.
If you want a true Philippine experience, try heading by ferry over to Bohol for a few days or heading out to her province if she lives within an hour or so from city central. I have hit the rural areas near Cebu and rented scooters for a pretty fun time buzzing around the highways which are practically deserted except for an occassional bus.
The Tabuon dried fish market is an interesting trip inside the city. It is a bit rundown, but the huge baskets of dried fish of all sorts makes for an interesting sight. Smelly, but interesting!
There are other posters that can direct you around Cebu much better than myself, but these are some ideas I had.