Algiers is a good base for day trips. The Roman ruins at Tipasa are an hour west along the coast — atmospheric columns and mosaics right on the Mediterranean. Djemila and Timgad, further east, are among the best-preserved Roman sites in North Africa, though they require an early start or an overnight stay.
Closer to the city, the Chiffa Gorge offers mountain scenery and Barbary macaques. In winter, the ski station at Chrea is about 60km south. The coastal drive west to Cherchell passes through beautiful mountain scenery, and the small archaeological museum there is worth a stop.