I am also a student in Senegal for the semester, and I've been in Dakar for a little over a month, so maybe I can throw some ideas at you.
There are definitely beaches; the Mermoz beach, walking distance (a bit of a longer walk, but doable) from UCAD (where he's studying, right?), is nice and big, constantly populated with men working out en masse. This beach is good and convenient, and I probably go about twice a week, but what can be obnoxious about it is how much you get hassled, just because you're white, guys will come up to you and just start talking to you, proposing marriage and the like (granted, you'll get proposals on the street, too, but at the beach it helps if you pretend not to speak French). There is a great beach near Oukam, which is much more secluded. It's safe and breathtakingly beautiful. It's also very close to the Mamelles lighthouse, which is a good reference point to give to the cabby, and also a lot of fun to visit. There's a restaurant at the lighthouse, too, but I haven't eaten there.
You should check out L'Institut Français. There are always exhibits and events, ranging from music to photography to films and dance. They have a library and a pretty swanky restaurant.
There is a place called New Africa that offers salsa lessons. I haven't taken the lessons, but friends of mine are and not only are they enjoying them, but I've been to the place on a Friday night and it's like stepping into a little world where toubabs, ex-pats, and locals come together to dance some amazing salsa, play billiards and eat great food. You might like to check out some sort of lessons while here, and though I don't know what L'Institut Français will be offering at the time, you could always go home with great salsa skills, or take mid-week lessons and then take your bf there on the weekends for dinner and dancing.
There's always live music and dancing in Dakar, just look at places like Just4You (which I have yet to go to) and see what you can find.
Oh! And for a day-trip, Ile de Madeline is spectacular.
As far as being a woman alone in Dakar, you can manage it as long as you can be comfortable with you surroundings, don't let random people bring you anywhere, and don't walk around alone at night-especially on the corniche! Cabs are always worth it at night. The standard Saturday night lowest-price-you'll-get is 1500 (about 3$), but during the week you can always barter lower, if you're going somewhere within Dakar.