The number one building that stands out (literally) in the city's skyline is the Mole Antonelliana. It is one of Turin's biggest symbols, housing the National Cinema Museum, the world's tallest museum! It is extremely well-thought-out and impressive, taking you on a journey from the first lenses to the biggest blockbusters.
You can also take the panoramic lift (which passes through the main space of the museum) to get to the top of the building and enjoy the views over the city, but be sure to reserve your spot in advance (see the link below).
I loved visiting this museum, but I'd recommend trying to avoid the weekends as it can be much more crowded.
Admission is €18 for the museum and €9 for the lift. If you don’t purchase the city card, get the combined ticket to the museum and lift for €20 (in the link below under Admission Tickets). If you do get it, buy the museum and lift ticket seperately (in the link below under Museum Pass and Torino+Piemonte Card Admission Tickets) – the museum is free to visit with the card and the lift ride gets a small discount.