We took our 18 months' old son to Majorca - Magalluf in 1982 ... it was a success, but maybe nowadays Palma Nova would be better as it has a much more enclosed and shallow beach.

Alcudia, in Majorca is perfect for young children........... the sand on the beach is white, the sea is crystal clear, and goes out for ages not getting any deeper, so very safe even for the youngest of children. Most bars and restaurants in Alcudia have a childs playground, or some kind of activity for children next to them, giving parents a little "chill out" time, while there children play safely. Cyprus is also very child friendly, lovely beaches, but is double the air time journey. Majorca takes around two and a half hours, Cyprus just over four and a half. Good luck!! You will have a lovely holiday if you book either of these destinations..........

We also went to Magaluf with our son when he was 16 months - Hotel right on the beach - (Iberostar Magalluf beach but think its now called Majorca beach or it could be the other way round, sorry )
We went in October and it was lovely - quietish with none of the rowdies around.
The hotel was a family friendly sort of thing via JMC I think but 4 years ago so may be different now.
We had a fab week-a nice easy holiday.

OK thanks guys. We'll have a look at packages to Majorca.

In then meantime though has anyone got any ideas for my original suggestion of places in mainland Spain?