UKC

I was thinking Costa Blanca but looks like it's borderline temperature-wise at end of May. Any recommendations? We're completely out of shape so my mate in particular will need a plethora of 4s and 5s and I'll need a plethora of 5s and low 6s.

You might investigate the Inn valley west of Innsbruck or The Ardeche or the Asturias and Cantabria provinces of northern Spain.

Orpierre? It’s gonna still be hot but defo doable. Plenty to go at all the grades. 

Provence is nice at that time. Dentelles de Montmirail and Buis les Baronnies areas have loads of stuff in those grades.

The Ariege area is worth considering:  Auzat and  Calamès are very good for easy grades, there are other options in the area too, and it's not all limestone!  

+1 for Calames. Sector Papy has a score or so 5s and 5+s which are all good. Some are billed as 40m long single pitch though with some care you can scrape by with a 70 m rope.

Sardinia. Can get hot in the sun though, but there are plenty of crags with shade or pick your time.

PS. I see your looking for 4s as well as 5s. Sector Initiation is very close to Sector Papy and has several nice routes given 4 or 4+ but mainly about diff or v diff. Very flattering.