The tower you can climb at Cádiz Cathedral is the Torre del Reloj, the eastern (Levante) tower, not the Poniente tower that some older pages describe. It is a self-paced climb to a viewpoint, not a guided tour, and the ticket is the same one that gets you into the cathedral itself.
What the ticket covers
The city tourism office lists the general ticket at €10, and it includes the cathedral, the crypt, the clock tower viewpoint and the Casa de la Contaduría, which houses the cathedral museum. Its concessions: over-65s pay €9, students aged 13 to 25 pay €8, natives or residents of the diocese pay €5, and children under 12 go in free.
The crypt is worth the few minutes it takes. The composer Manuel de Falla is buried there, which is a good reason to do the cathedral first and the tower second, as the building intends.
The climb and the view
After the cathedral visit, the tower entrance is on your right as you leave the building. The towers are the highest points in the city, roughly 54 metres above the ground and 58 metres above sea level, and the clock tower was finished in 1845. The octagonal towers rise in three bodies, the first Baroque and the upper two Neoclassical.
From the top you see the whole city laid out on its peninsula and the Atlantic beyond it. The clock itself, a piece by José Manuel de Zugasti, was restored and can be seen by visitors. One practical warning: the bells sound every 15 minutes right above your head and are painfully loud, so keep an eye on the time before you linger by the bell level.
For a second vantage point, Torre Tavira offers a different angle over the rooftops. Doing both is a reasonable way to spend a morning, since the cathedral tower comes bundled with the cathedral ticket.
Hours and timing
The city tourism office lists the clock tower as open Monday to Saturday 10:00 to 20:00, and on Sundays 12:00 to 15:00 and 16:00 to 20:00. The last climb is 30 minutes before closing. Hours can change for liturgical needs, and the cathedral interior follows a different Sunday pattern (Mass is at 12:00 and the interior opens afterwards, so confirm the time), so plan the cathedral and tower as one visit on a weekday if you can.
The tower is not a long climb to plan around, but the full cathedral visit takes a while, so give the pair of them most of an hour at minimum. Check the cathedral's official page before you go for seasonal changes and special events.
Pairing it with the old town
The cathedral sits on the edge of the old town, so the tower fits naturally into a walk through El Pópulo and Santa María. Afterwards, a plate of pescaito frito at one of the nearby bars is the obvious reward, and in the evening a flamenco show rounds out the day.