There's lots to do in Bordeaux. The tourist office runs half day and full day wine tours to the areas in the region - I did the Saurternes one last year and would recommend it. There is a school of wine (near the tourist office again, can't remember the name off the top of my head) and you can do wine tasting courses, etc. here.
St. Emillion is about 45 mins of a drive from Bordeaux, beuatiful little village/town, lots of wine tasting, good restaurants. St. Emillion is a day out and I'd highly recommend it even if you're not a wine buff. there a tower/castle with a viewing point - spectacular views of the surrounding countryside.
No shortage of good restaurants in Bordeaux from the cheap and cheerful where you can get a menu for 15-20 euro, to the more upmarket expensice ones. One in particuliar I enjoyed while there was across the river from Place de la Bourse, I think the area is called La Bastide, the restaurant is on stilts out over the river, really nice. The name escapes me. Place du Parliament has some good small restaurants that are very reasonable.
You can hire bikes from the tourist office. its an easy enough city to cycle around, down around the hangers is a good place to cycle, they have some nice bars and shops down here.
Also, Bordeaux has a number of very good museums, I can dig out the details at home and post them here tomorrow.
I lived in Bordeaux for 3months last year and fell in love with the city, going back in 3 weeks for a long weekend and can't wait!