I recommend a walk along the Guadalquivir river. Seville looks nice from the river, when it is lit up. Also, the river area is usually very quiet at night compared to other parts where there may be too many tourists.
At night, Sevillanos like to go out to La Alameda, which has fewer tourist crowds. Alameda is a nice and large garden kind of place with tapas bars, Arabic style tearooms and is also a gay friendly part of Seville. Sometimes you will find live performances in La Alameda. Apart from La Alameda, I also recommend the Calle Betis area, which is full of bars overlooking the river.
If you like bars, I recommend "Clorofila" at night, after dinner. It is very beautiful and comfortable. It is a bit hidden, near the Torre del Oro, so you do not usually find tourists here.
Another of my favourites is the rooftop bar La Terraza de EME (rooftop of EME Catedral Hotel). You can have some delicious cocktails here accompanied by panoramic views of the floodlit Cathedral and Giralda.
Seville nightlife areas
Santa Cruz has NO nightlife
Santa Cruz is nice to walk around during the day and see the historic attractions but it is not a place for nightlife. Stay away from Santa Cruz in the evenings if you are looking for a buzzing area to hang out.
Calle Betis has good nightlife
Located along the river on the Triana side, C/Betis is lined with bars. Some bars have very sought after terrace seating so go early to get a spot.
From a convenience standpoint, Plaza Alfalfa is close to the attractions and has a lively atmosphere in the evenings. It has good restaurants, bars, and cafes. This would be a good area to stay as well.