Seville Cathedral (and taxis) the world’s largest Gothic church.
Naturally the city’s pricey horse carriages are primarily for romantics or extravagant tourists.
Seville’s historic centre is large enough to need a few days to explore but small enough to do the exploring on foot, though rental bicycles are a good way to get a broader and faster look.
Ask at hotels (the bugcrew had rentals delivered to the hotel at no extra charge).
Alternatively if you have the time, inclination and a credit card the city offers rental bikes from various automated locations with information in English.
Trams run through the upper corner of the old town but the route is not especially useful for regular tourism. There’s also a Metro stop at Puerta de Jerez in the old town which cleverly does not connect with the main Rail Station of Santa Justa. So that’s a long walk or a taxi ride then.