I am from Basel and grew up here so I can tell you something about the nightlife in Basel. But to be honest..... most of the times I go to zürich to party.
Well, my favourite spots in Basel are "Das Schiff" (good place to meet people and good sounds) "Presswerk" in Münchenstein (also a good place especially for the drum n bass fans), "Bar rouge" in the Messeturm (especially on Thursday a bit older crowd, 25 up), "Kupple" ( but go only to the 25 up parties otherwise you will have to deal with a lot of teenies).
These are the places I go to, there are much more, oh yes I forgot, "Nordstern" at Voltaplatz is also good.
Have fun in Basel and if you ever need a guide, you may contact me