There are countless bars and clubs in Tijuana offering all-night partying. The doormen are pretty aggressive about getting people inside, but there's nothing wrong with just strolling around until you find a place you like. Or just check out as many as you can like I did. I can't even keep track of how many difference places we saw in two nights.
Cheap beer is good beer in my book, and Tijuana has plenty of that. The bars have tones of crazyness going in them most nights. If you plan on partying in Tijuana, bring a healthy liver and make sure you don't too out of hand - you are still in another country and there's a lot of desert for drunken people to get lost in.
Dress Code: As long as you are not naked, party on.
Listen, there's no end to the nightlife in Tijuana. You can take a bus from San Diego, CA accross the border for the specific purpose of partying until dawn. Go to the Calle Independencia (if I remember correctly!) for all the gringo hangouts.
Dress Code: No jeans, tennis shoes, or sportswear. It's all about impressing the opposite sex, so skimpy clothing seems to be the rule (at least for women)...