From Santa Chiara, take Via Benedetto Croce to Piazza San Domenico Maggiore. On this square you'll see an obelisk built by the monks of San Martino after the plague of 1656 in which many people of Naples died (the monks saved themselves by shutting themselves inside the monastery). As you face the square, the building on the left is Palazzo Petrucci, the oldest building with its original entry and courtyard. Farther back is the entrance to the church of San Domenico Maggiore.
Inside the church you'll see remians of the original 10th century Romanesque church, early Renaissance art including important frescoes by Pietro Cavallini and copies of works by Caravaggio and Tiziano (originals are in the Capodimonte Museum). Tombs hold many members of the Anjou dynasty and the church also has the 13th century cross that's said to have spoken to Saint Thomas Aquanis.
San Severo Chapel holds major 18th century sculptures and paintings, including the Veiled Christ by Sanmartino. Current opening hours are 10:00 Wednesday through Monday and closing at 17:40 on weekdays and 13:10 on weekends (check current hours); Via Francesco De Sanctis, 19/21, off Piazza San Domenico Maggiore.
Coffee stop: Caffetteria San Domenico on the square is a good place for a coffee.