Canary Islands works well. Not long flights and great all inclusive packages. We loved hotel Gran Castillo Togoro Family and Fun in Lanzarote. Good buffet, fun slides and you can book Merlin rooms for families with kids which come with toys, cot, tent etc. We have been like 3 times!
Though never been in May so I can't comment re weather
Depends what you are looking to spend. We’ve done the euphoria in Crete lovely room and very modern hotel great for young kids with a good slide area but beach is a bit stoney. The Eden roc in Rhodes is lovely as well, beach was nice and calm, staff were amazing hotel itself not as modern but had a few different restaurants included. Many places in May can be cooler and pools can be cooler. We did Cyprus in 2023 end of May and the pool was really cold my friends were in Kos same time and said same really cool at night and couldn’t swim