4-5 days in Tunis in April

Planning a 4-5 day stay in Tunis as part of a larger Rome-Tunis-Gascogne-Dordgone-Paris trip in mid-April.

Primary interests are archeological sites by day, cultural exploits, scenery/light hikes. Not at all interested in spa, public pool, etc. Itinerary includes Carthage/Bardo Museum, El Jem, Dougga. Probably not much else unless we extend the trip (we can).

Ordinarily we would be looking for a self-catered/unserviced villa on Airbnb or similar, but not really finding anything we like yet. Plan B is a suite in Four Seasons or The Residence. Both seem to be large, sprawling hotels with focus on public spaces - not necessarily our preference. Given our interests - which one would you recommend, or if we value privacy, space, and lower-key luxury, perhaps something else?