Side Trip from Madrid

Have you entirely ruled out Spain? Late May is such a lovely time to be there and a weekend is so brief--I would make the most of the time you have and choose somewhere you can easily get to and from. It sounds like you like outdoors also, and while they are not coastal, two of my most favorite experiences in Spain were two brief trips in opposite directions from Madrid--Cuenca in La Mancha and Caceres in Extremadura. Both had numerous nature/hiking opportunities that I can share if of any interest. Are you okay w/ driving?
Otherwise, I would use skyscanner or whatever flight website you like to scope out direct flights from Madrid. It might be a good time to check out Mallorca, although I would want a longer trip there.
Good luck!

SInce you have a decent amount of time, I would suggest Sevilla. Walkable and great food and sites including the gorgeous Alcazar, Cathedral, and Plaza de Espana.

I would spend more time in Spain
Sevilla would be my choice

Or somewhere you can fly quickly and direct that also gives you a departure flight home like Lisbon

Granada. It’s an easy train ride from Madrid and has a completely different feel. It might be difficult to get tickets to the Alhambra at this date, but you could try getting a private guide to take you. Well worth it.

Another option would be Stresa, Italy. It’s about 45 minutes from Milan. It’s gorgeous.

I would stick with Spain...Sevilla and/or Cordoba. Beautiful and intriguing, both of them!
If you want a different country, then Portugal, either Porto or Lisbon. Fun and different from Spain.

I love Granada and am indifferent to Seville (sacrilege on this board!), but with your likes and preferences, I would think you would find Seville terrific. (Sadly, I am not an Italy lover despite trying very hard, multiple times in multiple locations. I, personally, found the "vibe" of Seville similar - just giving you my point of reference and why I think Seville might be a location you would enjoy)

Highlight Options:
Royal Alcázar - check ticket availability,
great alternative for Alhambra (the Alcazar was based on the Alhambra)
as Alhambra in Granada is likely sold out (as noted above)
Cathedral - stunning
interesting old neighborhoods
Plaza de Espana
many other spots close at hand

An easy day trip to Cordoba to see the Mezquita if this is of interest - unique. And, Cordoba's old city is charming to wander.

Nice dilemma you are contending with!!!!! Enjoy whatever you choose!

Valencia would be another excellent choice. Too few travelers put it on their itineraries.

Vote for Toledo. Different but easily accessible from Madrid