Madrid to Barcelona, by way of... Seville, Granada...

5-6 nights and 4 towns is going to be rushed. I would encourage you to spend a night in Toledo - much better than just a day trip. 4N in Madrid gives you only 3 full days, and the first one you may still be in a jetlagged haze. So maybe spend your 5th night in Toledo, then take the train, via Madrid (no choice there) to Sevilla. I don't know if you can get a last-minute entrance to the Alhambra, and if you can it will probably be with a relatively expensive tour. If you aren't going to be able to spend significant time (4-5 hours minimum) at the Alhambra, it's not worth going to Granada. Also, the only reasonable way to get from Granada to Barcelona is by flying - and last minute tickets are likely to be expensive. If you choose Granada, then I'd definitely skip the hill towns. If you want to see Sevilla, you need at least 3N there.

Barcelona has lots of sights and activities and there are several excellent day trips as well. I suspect that the people who say "skip it, it's just a cruise stop" are those people who only visited on a cruise stop and didn't see the city. I am not a fan of Gaudi so, though I've spent a total of nearly 2 weeks in Barcelona on 2 trips, I've only visited the Sagrada Familia and still have a list of places to see and things to do on my next visit.

We had a great 17 day trip to Spain in October 2017. Here are my thoughts:

I wouldn't say "overzealous", but if you don't want to rush, you can't possibly see everything that you really want to see. You'll have to make some hard choices.

We chose Segovia/Pedraza as our only day trip from Madrid. I am very keen on Roman ruins and I wanted to see the Aqueduct there. The other people on the day trip raved about Cuenco. If you have time in Madrid, visit the practically free Naval Museum, if only for the first known map of the Americas.

I didn't expect to love Barcelona, but I did. Don't miss the Saint Pau Modernista site just a 10 minute walk from the Sagrada Familia.

If it weren't for the Big 3 Museums in Madrid, Seville would have been my absolute favorite place. Compact, and loaded with fascinating things to see. Favorite hotel - the Becquer, and restaurant - El Baratillo, of the entire trip. A day trip to Jerez de la Frontera and Cadiz were icing on the cake.

https://www.tripadvisor.com/Attraction_Review-g187497-d1192272-Reviews-Recinte_Modernista_de_Sant_Pau-Barcelona_Catalonia.html

https://www.hotelbecquer.com/en/

http://www.barelbaratillo.com

Thanks Chani, that helps! Good point on Granada as well.
Question: if we can't get tx to Alhamra, but we're only able to go in the parts of Alhambra that don't require tix, do you think it's worth going then? Or should we "save it for our next time in Spain") mindset? ( does the part of Alhambra that requires no tix for entrance, make it worth the trip to Granada?)
And Barcelona, as a matter of fact, you're right!! It was cruising people, or otherwise people that said they flew in/out, and didn't spend time there (beyond a day or so). I'll read up, and plan to love it.
Thanks for your help.

Thx Trayla,
You're totally right. I need to slow the pace, which requires Hard choices!! But yes, I do believe in slowing down and enjoying where you're at, versus rushing to check everything off the list.
And wow! So stoked you shared that advice, and those links-- the modernista de Sant Pau looks amazing!! I would have skipped it!! I need to stay open to Barcelona. Thx.

I honestly don't think it's worth the time, trouble and expense to go to Granada if you can't visit the Nasrid Palaces and the Generalife.

Here are a few things I really enjoyed in Barcelona:
Palau de la Musica - same architect as San Pau, book the tour and be sure to spend a few minutes in the cafeteria as well (BTW, prices are reasonable).
Rooftop tour of the Church of Santa Maria del Mar (the church interior is also well worth seeing)
The TI Moderisme tour - it will open your eyes to the wonderful architecture.
MNAC - art museum, be sure to allow enough time!

If you're there on Sunday, the City Hall is open to the public and free from about 10-1. Beautiful interiors. There's an underground museum with a thousand years (maybe 2?) of Roman ruins, part of the City Museum complex. The Hash Museum is interesting, also a nice example of modernisme design - no samples, though.
Day trip to Figueres and Girona. Start with the Dali House and Museum in Figueres, then backtrack by train to Girona with its cathedral (and beautiful cloisters) and a very well-preserved medieval Jewish quarter, and an excellent Jewish Museum detailing life in the Middle Ages.