My husband and I have an upcoming trip to Spain. Our itinerary is Cordoba (1 night), Seville (4 nights), Grenada (3 nights), Madrid (1 night - we fly in and out of Madrid). We are getting around via train between cities. I would love day with a moderate level hike (no more than 5 hours) with nice country side views and white villages. We have a lot of plans for Seville but have 1 open day we could do a day trip somewhere. Currently I'm thinking about using 1 of our days in Grenada to rent a car for the day (husband would prefer not to take bus) to head to Alpujarra region. I've done research on the website treksierranevada.com which is a very helpful. We don't want to spend much time in transit to get to hiking areas though with limited vacation time so are there other regions or national parks near Seville or Grenada that we should be looking at that may be better or just easier to get to?

One option: take a bus from Granada to the Poqueira Gorge in Las Alpujarras, spend a night in one of its villages, and return by bus the next day. That should meet all your needs -- moderate level hike(s), nice (actually, I'd say some rather stunning) views, some charming white villages that I believe are still off the beaten tourism trail (but it's been a while since I visited, and things do change).
High Alpujarra guide - restaurants & activities in Capileira & Bubion