The Island has amazing different geography.
The South coast has gorges leading to white sandy beaches (Cala Galdana, Cala'n Porter, Son Bou), the North coast is more rugged and greener (Playa Fornells, Arenal D'en Castell, Cala Morrel)
The resorts near Ciutadella (West) are very built up and commercialised and have no beaches to speak of.
Punta Prima near Mahon (East) is small, pretty, good beach and quiet.
I think Cala Galdana (middle of the South Coast) might appeal to you, very scenic, horse-shoe shaped bay, lovely beach, restaurants, not a lot of night-life and you can walk along the coast to some of the amazing virgin beaches nearby.
Here are the resorts and what I think of them (I've been holidaying in Menorca for 10 years now and know the place inside-out), but I am sure others have their own opinion different to mine.
Arenal D'en Castell - very pretty, a bit "English", 3 large AI hotels, good for kids
Cala'n Porter - again pretty, resort is set above the beach, again a bit "English"
Cala Galdana - beautiful, fairly quiet on a night, busy in high season
Cala Morell - stunning lunar landscape with burial caves, good snorkelling
Playa Fornells - a couple of km walk away from the stunning fishing town of of *Fornells, OK beach, mostly private villas and apartments, a couple of decent restaurants.
Punta Prima - white sand, lots of other resorts nearby, quiet, decent food.
Son Bou - 4km of white sand (best beach on the Island), scenic, more to do on a night, but still not busy. Next to Santo Tomas, small and popular.
Cala'n Forcat / Blanes - no beaches really so have rock platforms for sunbathing, quite built up, near Cuitadella.
Cala'n Bosch south of Cuitadella, a bit "English", popular, more to do, has a marina which is nice to wander around.
The weather in May should be OK, but Menorca is one of those places you just cant guarantee it (our last 2 weeks in July were a wash-out). And when I say a bit "English", I just mean there is the occasional place selling fish and chips and fried breakfasts, nothing OTT.
Enjoy.