The city of Bordeaux itself is architecturally fascinating. It is somewhat centrally located, with the Medoc region to its north, St Emillion to its East, and the Graves/Sauternes region to its south.
There are a number of GREAT wine bars. The "Bar à Vins" right next to the office of tourism in the City Center serves Bordeaux wines exclusively, and is a great way to try wines from all of the regions you didn't get a chance to visit. The prices are VERY reasonable. Ranging from TWO to EIGHT euros a glass, and you can even get a "tasting" size--half the wine for half the price! I tasted 6 wines for 11 euros.
Another great wine bar is the "Aux 4 coins du vin." They also serve different sizes--ranging from a true "taste," to half glass, full glass; or bottle. The smallest 3 cl is great to taste a really expensive wine. It is less elegant and more trendy than the Bar à Vins, but really fun in its own right. It is self-serve, so you put money on a card, and then use the card to sample the various wines. Kind of like a soft drink machine!
Lastly, don't forget to try the Lillet, the aperatif of the region. It is definitely stronger than wine, but very fruity, and the orange zest adds a nice spunk!