Seville in 3 days - what do you recommend?

Hello, not sure about your interests, but I'm a huge Roman history buff, so I would probably day trip to Italica, it consists of the ruins of a major Roman city, both Roman Emperors Trajan and Hadrian were born there, and more recently Game of Thrones filmed extensively there in the amphitheater.

Complement a visit to Italica with the Archeological Museum of Sevilla, where many of the treasures of antiquity are displayed.

Also if you are not already spending some time in Cordoba that would be my highest priority in terms of day/side trip.

Here is what we did with 3 days in Seville:
--walked to Plaza de Espana and recreated a scene from a Star Wars movie
--walked back from the Plaza to our apartment (near the Cathedral) to enjoy the city
--attended a flamenco show at Casa de Memoria
--went to the Cathedral
--went to the Alcazar
-- took a bus to the Macarena church and discovered it was closed. Took the bus back to the Triana area and walked around.
-- Walked from Triana area back to our hotel
--Ate some awesome food in Seville (La Azotea, Torres y Garcia)
--walked around the city a lot!

I felt we barely had enough time to really enjoy the city. It's a great place!

Wow Nick that was really helpful. I am buying my ticket to Sevilla's alcazar today, and planning my days out in better order thanks to you!

To me, the big three are the Alcazar, Plaza de Espana, and the cathedral & Giralda tower. Maria Luisa Park is nice for a stroll, and a walk along the river, walking by the Torre de Oro, is nice. Then there are the other places Nick mentioned. It’s been decades since I visited Italica, but thoroughly enjoyed it. If it’s your first time in Sevilla, you’ll have no trouble filling 3 days.

This is what we did in 3.5 days:

Day 1 (arrival day): Walked through Jardines de Murillo and slowly made our way to Plaza de Espana (absolutely beautiful!)
Had gin tonics to cool off at Maria Luisa Park.
Dinner at La Azotea in Barrio Santa Cruz. One of our favorite restaurants.

Day 2: Visited the Real Alcazar. One of the highlights of Seville. Just as stunning as Alhambra, IMO. Spent about 3 hours here.
Visited Triana neighborhood (very interesting area).
Dinner at Mercado Barranca.

Day 3: Decided to visit Triana again, and walked there, so got to see some other neighborhoods along the way. Lunch at the Mercado de Triana.
Visited Casa de Pilatos. It's a hidden gem! Very beautiful and not crowded at all.
Horse and carriage ride to Plaza de Espana.
Dinner at La Azotea again.
Saw flamenco show at La Casa del Flamenco.

Day 4 (our last day): Visited Seville Cathedral and the Giralda.
A lazy afternoon: lunch at Mercado Barranca again! Got drinks at nearby bar by the river, and stayed there for 3 hours! This was the end of a month long trip, so we needed to relax! But there are certainly more sights we could have seen in Seville.
Dinner at Bar la Catedral.

Seville is a gorgeous city architecturally with lots of fountains, plazas, parks, etc. We stayed in Barrio Santa Cruz and loved wandering around there.