The best months are April–May and October–November, when the temperature is comfortable and the sky usually clear. Summer (June–August) can be brutally hot — there is almost no shade on the site — and the light is too harsh for photography in the middle of the day. Winter visits are possible but the site can be muddy after rain and the wind on the exposed hillside is bitter.
If you can time it, come for sunrise: the gates open at 8am, you will have the place almost to yourself for the first hour, and the slanting light makes the limestone glow. The Dougga Festival in late June and July stages classical performances in the Roman theatre — a memorable evening if your dates align.