The 17th-century Palazzo Carignano is one of Turin's UNESCO-listed royal residences, once the home of the princes of the House of Savoy-Carignano and the seat of the first Parliament of the Kingdom of Italy.
Located in the lovely and lively Piazza Carignano on Via Accademia delle Scienze, it's also one of the most gorgeous Baroque buildings in the city and a fantastic photo spot.
I haven't visited it on the inside, but it is possible to make a reservation for a guided tour (only in Italian at the moment) to see the Apartments of the Princes (Appartamenti dei Principi) - see the link below.
Admission is €5, but it's free to visit with the Torino+Piemonte Card.