If you are a night owl, you will find plenty to do in Dakar after the sun goes down. From electronic music to Afro-pop to salsa dancing, there is something for everyone here.
Dakar is small enough that there is usually one 'main' party each night of the week where most foreigners and Senegalese head. This can be a blessing and curse, depending on how much you like to see familiar faces when you go out. Personally, I love it because I get to see all my friends whenever I go out and I always know what's happening on the weekend.
Another thing to know about Dakar nightlife: it starts late and ends early. Most parties only start filling out around midnight at the earliest, and can last well into the early hours of the morning. If you are not a night-owl, or just want a decent night's sleep, this can be challenging. I usually pick one night a week to go out since I don't have the stamina but plenty of people go out every night of the weekend!
Without further ado, here are my recommendations for where to go out in Dakar!
Thursday Night at Hotel du Phare
Each Thursday, the Hotel du Phare in Mamelles hosts a DJ set and dancefloor that can get surprisingly rowdy for a weeknight. This hotel/bar/restaurant has a beautiful rooftop and definitely young/hipster vibe. It is frequented mostly by French and European expats, along with a few (but definitely less) local Senegalese people. The music on Thursday nights is usually electronic mixed with some African beats and drinks hover around 3,000-5,000cfa. The downside is this party doesn't get quite started until at least 10pm, so if you have to get up early, it can be a bit of a late night.

Friday Night at Bayekou
Each Friday, the rooftop bar and Italian/Peruvian restaurant Bayekou in Ngor opens its doors to the weekend masses seeking a good drink and some dancing music. Bayekou is one of my favorite places for a Friday night because: one, it's more of a bar than a club so you can easily talk to friends (the music isn't too loud), two, it's located in Ngor which is near my house in Almadies, three, everyone seems to head there on Friday nights so it's easy to see lots of different friends all in one place, and four, it ends at 1am so I can be in bed at a semi-reasonable hour.

Saturday Night at the Lighthouse
Each Saturday night (and Friday night for that matter), the Lighthouse fills with weekenders looking to let off some steam on the dancefloor. The lighthouse is definitely on the swankier/more expensive side, with a 10,000cfa entrance fee after 11:30pm (it is 5,000cfa before) but the view overlooking the city and the posh ambience can make it worth shelling out the extra money. Lighthouse is always a safe bet in terms of crowds-- you will find a more upscale Lebanese, French, and Senegalese clientele. Go late and stay until it closes around 4am.

Sunday Night Salsa Dancing on Beach Road
Sundays are for salsa-- at least they are for me in Dakar. Most (but not all) Sundays, one of the restaurants along beach road in Almadies will host a Latin party in the early evening, usually starting around 5pm and lasting until 11pm. I always love to go, even if I can't find the courage to go out onto the dancefloor. This is a great, relaxing Sunday opportunity to watch some incredible (seriously incredible) dancing while enjoying the lapping waves nearby. In case it's not clear: the dancers in Senegal have some serious moves so you might feel out of place if you've never danced kizomba or salsa before. If you want to learn salsa or kizomba, Dakar Latino Club (DLC) has classes for beginners on Thursday nights at Complexe Hibiscus.

And Some Honorable Mentions
There are lots of monthly parties that happen in Dakar at varying locations. There is Electrafrique, which usually happens once a month and takes place in Medina. There is Fool Moon Party, which happens in varying locations and only happens in the summer months. There are occasional parties at Relax Beach in Alamdies, SeneSurf in Virage, and at The Hub in Point E. Usually these parties are posted on Facebook Events, so keep an eye out! There are also always new places opening and closing in Dakar so it's hard to pinpoint which the 'best parties' or 'best bars' are since they're always changing!