The Constellation Club, forward on deck 11, is the Infinity's largest lounge, with dancing and drinking far into the late hours. The Rendezvous Lounge on deck 4 is a good place for a before or after dinner drink since it is next to the Trellis Restaurant, as is the combination Martini and Champagne Bar on deck 5. The quietest bar on the Celebrity Infinity is Michael's Piano Club on deck 4 near the Photo Gallery. Michael's was originally designed as a cigar bar, but is now the best place for a quiet drink such as a caipirinha, a traditional Brazilian cocktail.
Like most cruise ships, the Celebrity Infinity lounges have "drinks of the day" specials that match the day of the week (e.g. Monday is Flirtini, Manhattan, or Coyote Margarita day), and the Cova Cafe has a flight of wines tasting some afternoons. The Martini bar had a flight of martinis - six, 1-ounce martinis - one evening that we enjoyed. I always enjoy wine or drink tastings like these since it gives you a chance to try "something different", and the Infinity had both wine and liquor tastings onboard during our cruise.