Wouldn't necessarily recommend Menorca as a 'biking destination...it's as flat as a pancake, except for Monte Torro....
Roads not bad, big EU funded re-building programme underway at present....summer traffic consists mainly of foreign tourists driving unfamiliar LHD rent-a-cars whilst under the influence of sangria.......
I would, however, recommend Mallorca (ferry also from Barcelona)....a much bigger island with great 'biking roads to the north & west of Palma......it's easy to get away from the tourists and enjoy the fabulous scenery.....
(I'm biased, 'cos I lived there for a year after retiring from the eclop.....with just a R100RS fror company!!)
I have to agree with the Dutchman. Menorca is a really nice place for sailing and swimming but not for bikes. Theres only the one road from Mahon to Ciededella (spelling) which is a straight line.
Never been myself. I think it's a family holiday and he is going to ride down and enjoy it and then spend quality time with them, then have a nice ride home whilst they fly!