Hi,
We were in Menorca mid May for 2 weeks and can certainly recommend the following beaches,
Son Parc large beach and shallow water
Es Grau, large beach and shallow water, very good on far side, Es Grau is a quaint little village as well.
Cala Galdana great beach and reasonable shallow water, (reputedly best beach on the Island).
Cala Macarella near Cala Galdana, secluded beach a bit of a job to find by car but is only 20 minutes walk from Cala Galdana
Cala Pudent, 1 k. walk from Son Parc car park.
Calan a Porter great beach, houses built into the cliff.
Punta Prima we saw this one but did not try it.
Platja Mesquida, this one can be difficult to find some where to park and turn the car round, but it is a beautifull beach
Watch which way the wind is blowing from and try the opposite side of the Island as you have a car.