4 Days in Seville

Triana is a charming neighborhood, great places to eat, atmosphere, market.  Also, this is where you will find authentic pottery.  I believe there are only one or two places left that actually produce/make the pottery on site, be sure to ask.  We also thought the bullring tour was worth the time and price of admission.  

I would recommend a boat trip on the Río Guadalquivir , it IS a little touristy but it's nice to see the city from a different perspective. Definitely a walk in the Jewish Quarter and a tapas crawl down Barrio Santa Cruz. Try the oldest tapas bar in Seville El Rinconcillo for the character of the place and the lovely old tiles. Seville is a really beautiful city to just wander aimlessly in.

I agree with Peter about the Flamenco show. Our hotel booked it for us. Even though it was just around the corner from our hotel, we got lost on the way there! Part of the fun in Seville is getting lost in Barrio Santa Cruz. I loved walking around the "Kissing Lanes."
Another thing we really enjoyed was a carriage ride through the city. Picked up near the cathedral, we rode through the city, Parque de María Luisa (which, to me is a hidden treasure), and on to Plaza de España . 
I wrote an article about Seville at SushiandGelato.com The article is about things to do with kids, but really, the items are just as fun for adults.
Seville was a highlight of our Spain trip. You'll have a great trip!

I haven't been to Seville since 1983, but I'm guessing this particular aspect of the city hasn't radically changed, so...my wife and I were in the Jewish Quarter and someone came up to us and handed us a flier advertising a flamenco show at a club that evening. Our first reaction: Oh lord, what touristy trash. Forget this. But then the evening came and we didn't have a specific plan, but we still had the flier. So we went. And it was WONDERFUL. If you don't experience it frequently, flamenco is really soul-stirring, and apparently it's one of those things that isn't utterly defiled by having been packaged for clueless foreigners. Object lesson: Embrace your inner tourist rube and, every so often, just go for it. Sometimes it has its rewards.

There is a Seville city pass but, like all such passes, you should check whether you are going to use the majority of its benefits. I have found that city passes are rarely financially worthwhile unless you do so:
https://citypasses.eu/en/citytrip-seville/sevilla-city-pass/
You can buy a 1- or 3-day 'Targeta Touristica' for buses:
http://www.tussam.es/index.php?id=192
But, again, it's worth checking whether paying for fares separately will work out cheaper. It all depends on your plans.
There are a variety of other cards for the Metro, some of which include buses too:
https://www.metro-sevilla.es/en/tickets-fares