Hemingways appears to be the best place in the old city to get a cocktail (Mojito's are pretty good!). It has a nice location across from the Rectors palace and anyone who is walking round the old city in the evening is bound to come past.
On the down side, when I was there it didn't have much atmosphere and I suspect you'd want to bring a good crowd with you. Its not helped by the seductive sounds of jazz drifting over from the Troubador jazz club around the corner :-)
Dress Code: None that I could see
It's a cocktail bar, and they, like they will tell you proudly, ONLY sell cocktails. I had the best Mojito ever there! They have really comfy chairs, all facing the pedestrian streets.
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