Day Trips from Sevilla

MD train to Cadiz takes a little less than two hours each way, but only if the weather is mild. Ditto Huelva.
Fact is, you can find enough nearby in Sevilla to keep you busy.
I'll let other commenters rave about Cordoba!

Thanks for your advice!

After Sevilla, I spent a couple days and nights In each of Córdoba and Jerez de la Frontera, and enjoyed both very much. Each is just an hour or so from Sevilla by train, so can easily be day trips as well. I also spent a day in Cadiz on the coast, less interesting to me, but it was the very last day of my trip, and my reaction may have come from tiredness or travel burn-out. Cadiz is about two hours from Sevilla.

If you can spare a night away from Seville, you can go to Granada to see the Alhambra. But I wouldn't try this as a daytrip from Seville. What you want to do is spend a night in Granada, and book your Alhambra admission for the morning after you arrive. This way, you're sure not to miss seeing the Nasrid Palace (you get a 30 minute entry window and they are very strict). Since it's about 3 hours each way between Seville and Granada, this doesn't work as a day trip.

Yes, Cordoba is the obvious daytrip from Seville (AVANT train is just as fast as AVE train and much cheaper). If you like Roman ruins, you can get a bus from Seville to Italica (I didn't find it difficult, but one of our other posters did).

Cordoba and Jerez are the standout choices.
Cadiz or Arcos de la Frontera would be next, with personal preference determining your choice.
http://www.planetware.com/seville/seville-day-trips-e-and-sevsur.htm

Cordoba - the Mezquita is a must-see, the Juderia is extensive and well preserved, lots more
Jerez - sherry bodega tours, horse show at the Royal Equestrian School (only a couple days a week)
Arcos - beautiful hill town (pueblo blanco) From the Jerez train station, take the bus.
Cadiz - some love it more than others. I enjoyed it as a day trip from Jerez, but I'm glad I based in Jerez, not Cadiz.

If you time it well, you can combine either Arcos or Cadiz with Jerez in a single day.

Do not underestimate the joys of Sevilla.

Thanks to everyone for your suggestions. Think we may wait until we get to Sevilla to make decisions about day trips. Many of you feel there is plenty to see just in Sevilla.

Several churches in Sevilla have become more visitor-friendly in the last couple of years, if you like going through churches slowly and with sufficient lighting, that can take up a good bit of time right there -- the Salvador iglesia has always been a hidden gem, now it's got a bit of polish to it. Read up ahead of time on the relevant saints!

Cordoba is an easy day trip and the Mezquita was the most interesting thing we saw in Spain:
https://janettravels.wordpress.com/2013/09/27/the-mezquita-at-least-the-catholics-had-the-good-sense-not-to-destroy-it-when-they-desecrated-it/
I would make this a must see.