Rough itinerary for May trip??

You have listed areas that are geographically separate, so consider the time of travel between them.

Madrid- See the Royal Palace and the Prado Museum as well as Plaza Major. Also, do day trips to Segovia and Toledo.
Recommend 4 day minimum.

Seville is amazing, consider 3 day minimum. Do Cordoba in route for at least a day. Not sure why you want to skip Andalucia, an amazing region.

Barcelona and area is great, need 4-5 days. Do Monserratt and nearby towns from Barcelona.

Other great places in Spain are Salamanca, the Basque Region near France, Granada, Rhonda and Malaga area.

I guess I’m a little confused. We were skipping Andalucia because it’s out of the way and the travel time to get to the places like Seville is a bit long. We aren’t interested in the Alhambra. Maybe someday we will return and visit that region alone. From prior advice we were informed Valencia is on the way to Barcelona and Girona is something that can be done from Barcelona and can be an overnight or a couple nights with Tossa Del Mar as a day trip from there or even Barcelona. Not all the places I listed were a must. Just was looking for feedback on any of those places. We’ve been to France and plan to return so again maybe Malaga on another trip but that’s also slightly out of the way given we’ve only 13 nights total.

The only extra travel time would be Madrid to Valencia. In the overall itinerary that is probably only a few hours. I can only guess that the geographically separate comment was made because Valencia is southeast of Madrid while Barcelona and Girona are northeast of it. Sevilla would be way out of the way for where you said you wanted to visit.

I think your plan works well and you’d have sufficient time to get a good feel for the places you want to visit. Regarding Toledo, I feel it is best to spend a night, but others will disagree. If you did decide to spend a night I’d do it at the beginning of the trip so as not to split your Madrid stay. Visiting Toledo at the end of the Madrid stay would add travel time to the Madrid - Valencia leg of the trip since you need to go through Madrid from Toledo to go anywhere else.

Peniscola is nice! We stopped for a few hours on a road trip. The pretty part is quite small so a stop on the way or max one night would probably be enough.
https://slowtravelitalyspain.blogspot.com/2018/11/day-54-peniscola-and-salou.html
We also liked, on a different trip, Tarragona