That's a very good trade! You're in for a treat, Son Antem is our favourite resort although I know it's not to everyone's taste. It is a bit rural but that's fine when you have a car. It's an easy 20 minute drive from the airport, the closest town is Estepona which is a five minute drive from the resort. Here there are some good restaurants in the main square however be warned......if you have no experience of driving extremely narrow roads in an old Spanish town then consider parking outside the old town or get a taxi. Driving aside you can find yourself searching high and low for a parking space in the old town during busy times.
May is an excellent time to visit. Don't assume it's not beach time, whilst the sea is not warm it will most definitely be sunbathing weather. We tend to go in May and October and it's perfect weather, not too hot and ideal for exploring the island.
Palma is my favourite Spanish city and there's plenty to see there along with some great restaurants (I don't recommend restaurants as it's all too subjective).
This is a worthwhile guide to 36 hours in Palma,
https://www.telegraph.co.uk/travel/destinations/europe/spain/majorca/articles/36-hours-in-palma/
Another iconic attraction is the old wooden train that runs between Palma and Port Soller. It travels through the Tramuntana mountains and provides some fantastic views. It can be busy though and parking is often difficult to find in Palm. I would recommend going on a day when there are no or few cruises docked and also pick up the train at Bunyola. This is a small town at the base of the mountains. You can park at this little station for free and it is from here that the journey enters the more scenic portion. Stop off a Soller and enjoy a great lunch at one of the many excellent restaurants.
Also in the mountains is the town of Valldemossa, another worthwhile trip.
https://www.seemallorca.com/valldemossa
Arta is another lovely old town which is dominated by a fortress at the top of a hill and inside is an old church. The views from the fortress are impressive and the town is full of narrow cobbled streets with museums, independent shops and plenty of restaurants. Nearby are the Caves of Arta, hugely impressive caves full of stalactites and stalagmites which can be viewed on guided tours. I would suggest visiting the caves in the morning and drive to the town of Arta to climb up to the fortress and then have lunch in the town.
I wouldn't bother with the Drac Caves. Very overrated and touristy. Whilst the caves themselves are impressive you're ushered rapidly though them by a guide ending up in an amphitheatre filled with benches. If you're unlucky enough to be amongst the first to arrive in this chamber you'll have a long wait, possibly up to 40 minutes whilst the room fills up before finally being serenaded by a trio of musicians being rowed in a boat across the underground lake in front of you. This bears no relevance to the caves and is simply a naff tourist trap. The stampede towards the narrow exit at the end is also frustrating. The Arta caves are a far better option.
There is a very good market at nearby Campos. The resort staff will advise you of when the local markets are on. Expect stalls of the most amazing cheese, meat and vegetables alongside independent shops selling a variety of artisan goods.
Mallorca is an easy island to explore and nowhere is more than 1 1/2 drive away. It's a real gem of an island and is often overlooked by many Americans who are keen on concentrating on the Spanish mainland.
You don't specify when in May you're going. We'll be there during the last week with a number of friends as it is the May half term so if you're there at that time then expect it to be busy and I'd like to apologise in advance for my noisy children. However the beauty of Son Antem is the individual pools per eight villas which means that the resort never feels crowded and very often you can be the only ones at the pool.
