Generally, there are no left luggage facilities in Tunis and it's really hard to find one. Here are some of the few places you can find luggage storage in Tunis.
Tunis Carthage International airport
Currently, there is no left luggage facility at the airport
You can try asking for luggage storage at the hotels in La Marse which are very close to the airport. Try checking at Golden Tulip Carthage, Regency Tunis hotel and Abou Nawas Le Palace
Tunis's main railway station. (Tunis Gare Railway Station)
This train station is in front of Place de Barcelone. The left luggage office is on the left side of the main hall just behind the police desk.
Luggage storage cost is TND 5 per locker.
You'll need to present your passport before they give you the locker keys.
Safety tip: For more secure storage, walk to Habib Bourguiba avenue, just 10 minutes away from the train station and ask for your luggage to be stored at any of the hotels along this avenue. Most hotels will agree at a small fee.
National Bardo Museum
If you are visiting the museum, you leave your luggage at the luggage office at the entrance since they don't allow any bags into the museum.
I'm not sure if they can keep your luggage for a few days, probably yes if you discuss that with the people at the luggage office and pay a small fee.