13-day honeymoon in Spain

flights to Barcelona are way cheaper from Sevilla than from Granada.

In case you were not aware, there are a few high speed/direct trains a day from Madrid to Granada ~3.5 hrs. Perhaps you can change the order, Madrid>Granada>Seville>fly to Barcelona.

Congratulations!
Since you asked for honest feedback as to whether you’re packing too much into the itinerary— here it is.
You’re jam-packing too much into the plan!
Remember this is your honeymoon. You want to be able to relax and enjoy your time together. When two weeks is scheduled like an episode from the Amazing Race, you need to slow down and chill.
Since you're into art, you’ll love Madrid and its great museums: the Prado, the ***Thyssen- Bornemisza and the Reina-Sofia art museums. The National Archaeological Museum in Madrid has an amazing collection on exhibit also.

Near Madrid’s Royal Palace in Parque de la Montana (“Mountain Park”) is a surprising attraction that seems to be an impossibility. It is a temple from ancient Egypt called the “Temple of Debod.” The temple was one of many Egyptian monuments that was going to be lost forever to floodwaters when the Aswan dam was built during the 1960’s.. Instead, the temple was completely dismantled in Egypt, which gifted it to the city of Madrid, where it was reconstructed block by block and stands today near Madrid’s Royal Palace. Toledo was Spain’s capital for centuries until it was moved to Madrid and it is well worth overnighting in Toledo so you can experience the romance of the night there and also see Toledo’s monuments floodlit at night. Beware of Mondays when many sites are closed.
Just Madrid and Toledo can easily fill 4 days, and remember you will be jet-lagged for the first day or two and that alone will slow down the pace at which you’re able to move around.
Seville is worth at least 3-4 days, including time to visit Cordoba. You could save time taking a high-speed train with Iryo, Ouigo Espana or Renfe from Madrid to Cordoba ( 1 hr 48 mins) and seeing Cordoba on the way to Seville if you check your luggage into a locker next door at the bus station. Seville is about 45 minutes from Cordoba by high-speed train. www.TheTrainline.com will show you all your options. The best ticket prices are to be found directly at the source- the train company’s website.
You also could first go to Granada on a 3.5-hour high-speed train from Madrid, then train or bus from Granada to Seville ( 3 hrs. by high-speed train or bus; buses much more frequent and much less costly) then fly to Barcelona from SVQ ( Seville’s Airport). That will streamline your itinerary. www.Movelia.es has bus schedules. Buy tickets directly from the bus company’s website for the best prices. www.Skyscanner.com or GoogleFlights show schedules and fares. There actually is a direct Vueling flight from Seville to Barcelona on May 18 for the incredible price of $15.
With 7-8 days to enjoy Madrid, Toledo, Cordoba and Seville at a reasonable pace, you’ll have 4-5 days remaining. That’s time to overnight in Granada and allot the remaining time to Barcelona. And, yes, Barcelona is a dynamic, exciting city with an endless menu of things to enjoy. Five nights in Barcelona last September left me wishing for even more time in Barcelona.

Have a great Trip!

Are all of your accommodations not booked yet? May is pretty popular in Andalucia, so that makes me nervous.

I always end up skipping Toledo because I have not spent a lot of time in Madrid and I dislike that you have to go back and forth from MAD, rather than convenient onward travel. I would play it by ear on the day trip. Cordoba has Jewish history also.
I also skipped Granada, and I adored Cordoba so I have no regrets--I'll try to get there one day. You have to make these hard decisions and pick what appeals to you the most. Skipping something is better than packing too much in.

Since you asked, I think you are planning too much. Your itinerary is possible, but it involves a lot of travelling and tiresome accommodation changes. For example, as you note, you will spend a big chunk of one day getting between Cadiz and Granada.

You could consider staying north in only Madrid and Barcelona, which will give you time to see each more casually, plus a day trip or two from each. And/or you could travel between Madrid and Barcelona with a stop in Zaragoza which gives a contrasting look to the two bigger cities.

If you want to include Andalucia, then I'd drop Cadiz/Jerez and concentrate on one or at most two cities. Sevilla meets the preferences for food, art and history. But not really nature - but there are options for a rural day-trip. Ditto for Granada or Cordoba. But with 6 or 7 days, I wouldn't try all three since you want to prioritise quality over quantity.

I understand the attraction for a farm stay, but don't think you have the time unless you cut back on the city parts. Instead have you considered staying at an urban paradore? Some are central in cities, but also are in interesting, historic buildings.

Here's my recent trip report covering most of the places you mention: https://community.ricksteves.com/travel-forum/trip-reports/trip-report-spain-november-2023

How many nights total do you have in Spain?

Is your flight into Madrid and out of Barcelona set or can you change it?

As much as I wanted to see Barcelona, I elected to save it for another trip and focus on Madrid and Andalusia this time. We had 14 nights. It turned out to be a good choice and as it was, we felt like we packed in a lot and were moving a lot.

You rate art high on your interests so 2 nights Madrid is not enough. The Prado is my favorite museum I've been to. Seriously, it's amazing. Madrid also has a lot of other top quality art museums that I didn't get to.

Since you're flying into Madrid I would continue on to Seville when you arrive (either connecting flight or train). Spend 4-5 nights Seville (daytrip Cordoba), 3 nights Granada, train back to Madrid for the rest of your nights and daytrip to Toledo. Fly out of Madrid.

Too much travel, checking in/out, packing/unpacking.
Either Madrid and north
Or
Madrid and south.

davebarnes said what I was basically trying to say, but much more succinctly LOL

You’re jam-packing too much into the plan...this is your honeymoon...relax and enjoy your time together...an episode from the Amazing Race...

Very good observation. With the stress associated with most weddings, you'll need (not just want) time to relax and decompress.

Love long and prosper!

Thanks everyone for your well wishes and very helpful responses! What a nice forum! I will cull it down and chill out on the itinerary.

It seems like most people didn't mention Granada too much, so I'm wondering if we can make that at a day trip en route to or from somewhere else. We mainly wanted to see the Alhambra and the Lorca house.

Not too much talk on Barcelona either.

I dunno, something about Cadiz really attracts me...it reminds me of one of the small Greek islands we visited a few years ago, Naxos. Quaint, beach town, slower lifestyle.

Wondering now if the move is: Madrid (4) to Sevilla (3) to Cadiz/Jerez (2) fly to Barcelona (4) with a day trip from Madrid and/or Sevilla.

Stop me again if this is crazy....

Madrid (4) to Sevilla (3) to Cadiz/Jerez (2) fly to Barcelona (4)

Did you check for flights from Jerez to BCN? Are they direct?
I like that better than your initial plan, but it could just be that it is more specific. The thing about forum replies is that while all are genuine human experiences, the replies are generally based on what people did and liked. I try (sometimes fail) to urge balance overall--not too much moving, balance city and small town. You have that here, even though you have the unfortunate fact of a flight in the middle of a vacation (my personal pet peeve). Being stick with into MAD and out of BCN there are just going to be tradeoffs if you want to include Andalucia. Because Madrid and Barcelona are both large cities with airports, you are likely to return to either, so if you want to shave days off them to make Andalucia work better, that is something worth considering. Another thing to consider is staying longer in both to do day trips or do a side trip from either.
Again, I'd be a bit concerned about accommodations. I hope you have some places at least scoped out. And congrats!

Have you been together a long time?
Some people like very slow, romantic, private honeymoons as an opportunity to bond. A non-stop "every day a new place" honeymoon can be a bit stressful if as a couple you are not already familiar with each other's styles, and comfortable with traveling together. Also, what if something goes wrong? Does anyone speak Spanish, and can you deal with contingency situations with patience?
How do you define "quality?" How is your budget?
For me, honeymoons are a splurge occasion, but not everyone thinks like that. I would highly recommend reviewing the Paradores website to check out unique, gorgeous and historic places to stay in Spain. BUT, you may not be able to reach all of them by public transportation.
Do you want to know a little more about Spanish culture, people, and so forth? Staying in several places a little longer allows you to increase knowledge in depth. If you you just want to check places off a list, that is a different type of trip, although I agree that packing and unpacking too much drives me crazy, plus having to constantly look out for my suitcases on trains and planes is never relaxing.
No place in Spain is really totally "touristy"--it is the high numbers of visitors in certain areas and at certain times that can feel overwhelming. Unfortunately, Spain has become so popular that it is now very crowded in many places--like Barcelona, like Granada, and like the beaches.

You also do not seem to have a real clear idea about why you want to see a city or a town--what are your Must-Sees and Must-Dos? I would never go to Cadiz because it reminds me of Greece--I would just go to Greece instead! You may need to do a little more research about the history and key attractions of each place.
I, personally, would just skip Barcelona and go from Madrid to the South. You can see a lot in the Madrid area (Segovia, Toledo, Avila), and equally so in the South so that you will use up your two weeks quickly.
Plan a future trip to Barcelona--maybe if you decide to cruise in the Western Mediterranean.
Best wishes!

Thanks everyone for your helpful tips and tricks!

I'm just gonna throw in my quick two cents! My husband and I (67 and 61) did a month in Portugal and Spain last year May-June. Started in Portugal and flew home out of Barcelona. Cities visited in Spain were Lagos, Sevilla, Cordoba, Granada, Madrid and Barcelona. Alhambra with it's Summer Palace were probably one of the most stunning places I've ever been. And the gardens at the Summer Palace--so romantic!
Finally, it might've been because we were nearing the end of our trip, but by the time we got to Madrid and Barcelona, the size of those major cities felt like I had left the charm and history of our vacation behind and we were now just caught up in huge crowds and modern shopping and high rises! Don't get me wrong, the museums and some of the parks were just gorgeous, but there was definitely a noticeable difference. If I did it again, I might have done our itinerary in reverse.
And congratulations! No matter where you end up, you will take home amazing memories!