We will be in Seville soon from a Saturday to a Tuesday and then onto Madrid. We are a party of six. I would like to take a day trip, maybe to White Villiages, Olive tasting and even possibly on to Rhonda. Other suggestions? I am assuming the best day for this would be Sunday as most tourist attractions/shops are closed. Also, I am wondering if we should try for a private, tourist company/driver, rather than Viator, as we would likely appreciate some independence when visiting Rhonda etc. We are also trying to choose between hotel and airbb's. I am finding with 6 of us hotels can be quite pricey. (Parents paying for adult children and significant others!!)
Your timing isn't quite clear, but arrive Seville Saturday and leaving Tuesday would be just two whole days and fragments on either side. I'm not sure that really leaves time for a day trip out of the city.
But other ideas could be Jerez or Cadiz.
Someone in these groups recommended veoapartment.com, a short-term agency in Seville. They've got larger apartments, 3+ bedrooms. (Some of their listings can be seen on airbnb/vrbo as well.)