Please advise on the itinerary

In my opinion, you want to visit too many places in the time you have. Barcelona and Madrid are fine, but you’d be doing Sevilla and Córdoba an injustice trying to see them as a long day trip. It wouldn’t make sense to try and do each as a separate day trip due to the time and distance involved. Neither is recommended as a day trip from Granada. With a tour to the Sierra Nevada, 4 nights (3 days) should be sufficient for Granada.

Your basic itinerary is fine, but those day trips.... YIKES. Way too many day trips, IMO

Barcelona:
I dunno of Sitges makes sense. We didn't go there. Barcelona itself has a TON of stuff to see and Montserrat burns a whole day, Figueres burns most of a day. Both are worthwhile, but it's I feel like you should pick one, maybe two of the three day trips.

Granada:
I think Granada is very doable in 2 days and it's very worthwhile. The touristic areas are really compact, unlike Sevilla. What are you most interested in doing/seeing in the Sierra Nevadas? Montserrat is very dramatic from a natural beauty standpoint if that scratches your itch.

Sevilla:
Sevilla is really awesome with plenty to see. I loved it but your time is short and it's a bigger city in terms of sightseeing. Take cabs to save time...well worthwhile.

Madrid:
Museums, history, Toledo day trip. I dunno. I thought it seemed like just another big European capital. I was happy to leave but that's just me.

Cordoba is missing. I loved Cordoba. We were there during the Patio Festival but I just loved the vibe of the place in general

I suggest that you look at train schedules to see if some of your day trip plans are feasible. I’m pretty sure Seville from Granada isn’t. Since the overwhelmingly must-see in Granada is the Alhambra, you could cut your time there to 2 nights, eliminate the Sierra Nevada, and add the extra 2 days to Seville. I think Cordoba can be done as a day trip from from Seville, though my preference would be for more time there. You need to decide whether the hassle of checkin/checkout or time spent on day-trip travel is the more onerous for you. My own rule of thumb is that 1.5 hours of transportation, i.e., 3 hours rt, is my limit for a daytrip.

Rather than flying in and out of the north and traveling south which is too much back tracking I would consider flying into Seville or Granada and out of Madrid. For me two big cites in one trip is one too many. I like Madrid way more than Barcelona so that is the one I would pick. For me Granada deserves 3 nights (or a lifetime) and always on the weekend as the town is so much fun then. Wedding parties, people dancing in the square, love it. Seville also deserves at least 3 nights 5 would be better, I would give it more if possible. Cordoba is two nights for me as a day trip puts you in town during the day when there is little charm, the evenings are great. Then back to Madrid for the remainder of your time. Since your going in May the hill towns will be green and filled with flowers, worth thinking about staying in the country and saving the big cities for winter. Enjoy your trip wherever you end up going I'm sure you will have a lovely time. J

Rosalyn's plan is excellent. I would put Cordoba as a priority (there's nothing like the Mezquita that I've seen - not even in Morocco) and the Juderia is one of the best preserved (and most walkable) medieval centers in Spain. Take an early train from Sevilla to Cordoba on your way to Madrid. Check your luggage at the bus station across the street from the train station. Get there as early as you can because luggage space is limited and there is so much to see in Cordoba.

This is fast paced but let's you get a good taste of Spain. It's rather like Italy, no one goes there only once.

Thank you very much everyone for your advice. Barcelona and Madrid are not changeable as we already have tickets. But I think I am going to rethink everything in between.

I suspect your new plan might not include Sierra Nevada, but our trip in June 2017 did. Our kids were young and I tried to include some days that weren't museums and buildings. We weren't driving so I found a small van tour to Sierra Nevada, made the reservation, and was done with planning.

That morning, the guide seemed surprised we wanted to go there in the summer, but dutifully took us to El Dornajo Visitor Centre. Another visitor at the center heard the discussion about where to go next and was an employee at a botanical garden, I think Hoya de Pedraza Botanical Garden. The garden was more wild than the US botanical gardens I've been to and the employee gave us a tour, which made our day. We wanted a stroll and to see the mountains and that's what we got. Sierra Nevada the town was where we had lunch, but we mostly saw condos and some lift lines.

From this forum, I'm sure there are better hiking options near Granada if you want something more strenuous. All I can suggest is that if you look into a tour, ask about exactly where they go or tell them exactly what kind of experience you are hoping to have.