At the beginning of my stay here I would go out to the hotel zone because that's all I knew. Of course there are nice bars there and many to choose from but the problem is they are far from downtown and usually more expensive (tourist trap). For example, a night out in the hotel zone can easily cost you 50 USD which might be ok if you're a big drinker because that's including an open bar. If you're like me however, and want to enjoy some good music and a few drinks this is way too much money. First of all there is usually no cover charge to go out in the city. And the drinks are cheap. You can expect to pay between 30 and 40 pesos for a beer (and that's usually a 2 for 1).
Some nicer places will charge cover on certain nights or have free entrance/drinks for girls on the ladies' night. There is a brand new complex on Bonampak Ave. called Plaza Peninsula which has a nice bar/lounge called El Barezzito and also a nightclub called Rush. El Barezzito plays Mexican music, some of it live, and is very popular. For Saturdays reservations are required weeks in advance. Rush plays electronic music (and they have a guy on a saxophone accompanying the DJ, it is really cool) and has ladies night on Thursdays. Both of the places have an open roof terrace with the view of the ocean.
If you want to dance to some Mexican and Cuban beats and hear live music I recommend Mambo Cafe which is at the bottom of Yaxchilan Av (close to Coba and Yaxchilan). As for an afterhours in downtown you can check out Skybar (which is part of the Blue Hostel and is located on top of the roof). Really nice place and if there is a good DJ you can expect to party till the morning sunshine, especially on Friday and Saturday. A Corona costs only 10 pesos.
Like I mention in my previous post, to take a taxi between any of those places will cost you about 25 pesos. If you don't speak Spanish just mentioning the name of a bar should suffice. Taxi to the hotel zone will be more, at least 100 pesos, so take the bus, which runs 24 hrs a day and is cheap.
As for the hotel zone I'll just mention the more popular club names. Most people will recommend Coco Bongo and so will I. It's a dance club, with an open bar and an amazing show. With impersonators of major singers and other artists you will definitely enjoy the show. Beware though, on busy nights it gets really crowded. Like when I went there on New Year's Eve. First of all it was a big sausage party (good for girls I guess) and second of all I was so squished that my feet were barely touching the ground. Really, it was that bad. They just cram everyone inside, no regulations on the limit. The show usually starts around 11pm but no big deal if you miss the beginning. All of it is awesome and it lasts for a few hours. Careful on the limitless supply of tequila lol!
Other clubs you might want to look up are: The City (house/electro), Maxim Beach Club (during the day), Dady'O, Seanor Frog, Bulldog Cafe (younger crowd), Pat O'Brien's (good for mardi gras), Basic (beware of water sprayed on the dance floor), Ultra Club and Terrace (electro), Bling (facing the lagoon) or Nectar (afterhours). Some clubs might also have "working girls" on certain nights so keep that in mind if a girl is very friendly, like at The Mix Lounge. Also, there is a specific day for each club, like The City is good on Tuesdays and Pat O'Brien's is good on Wednesdays. To find out what's good for a particular night head to Oasis Cancun hotel and ask one of the reps there.