Get the TGM train line from Tunis. La Marsa is the last stop. Trips cost less than 1TD and take something over 30 minutes.
The beach is quite nice, but is reputedly popular with locals from Tunis on weekends.
There is a mosque with a fairly interesting tower near the train station
Relax in a coffee shop
Center Sidi Bou Said for Languages (Centre Sidi Bou Said de Langues et d'Informatique) offers classes in many languages including French, English and Arabic, including Modern Standard Arabic (MSA), classical Arabic, Tunisian Arabic and the various dialects of North Africa, the Gulf and the Levant.
There is a fantastic restaurant literally above the water on the beach. A meal with two courses and a beer will run you just under 50 TD, but the impeccable service and view out over the ocean and down the beach is well worth it.
The O Bar at the Hotel Plaza Corniche is popular, as is the nightclub below (Only starts around 1AM outside of summer, mostly house music but a friendly DJ with much music who can likely play to suit your taste if you arrive early or with a large group. License finishes 2AM).
The unique Hotel Plaza Corniche is on Rue de Maroc, a few hundred metres up from the train station (from the station, walk back down the train line on the coastal side. you can't miss the entrance). Not cheap, but offers pleasant enough rooms and a simple breakfast gratis. Quite an experience!