I stayed in Bordeaux for 3 nights last summer before heading farther south to Bayonne, St. Jean Pied-de-Port, & into Spain. There are a couple of car rental offices in the train station. I looked into renting a car, but it was a bit too expensive for my taste, and my AAA membership didn't seem to make a difference in price.
As for wine tasting: I suppose with the car and the other poster's suggestions you'll be fine for self-directed touring. There are some bussed wine tours that leave from the front of the train station. You have to sign up & pay in the tourist office (also in front of the train station). I tried to do one on the day of, but it was sold out, so if you go that route make sure you sign up for one in advance (they have a list of the week's tours in the tourist office).
There are some restaurants by the train station, but I suggest walking farther into town towards the main square, or by the riverside, to find restaurants and cafes. Everywhere I ate I got good service, tasty food, and nice wine (of course). Some places even sell stogies, if you're into that sort of thing.
From what I've read in his books, Rick considers Bordeaux to be somewhat boring. It's not Paris, but it was a laid-back place to relax for a couple of days, and it fit my itinerary just fine (I was in Europe to walk the Camino de Santiago pilgrimage in Spain, and Bordeaux has a link to the trek - plus I love wine). I hope you enjoy it as well.
