Not sure how old your daughter is, but you can't beat a trip to the capital, Palma. .....catherdral, museums, shopping, old arab baths, more shopping....
there is also the mountain town of Valldemossa
for trips from Alcudia, try No Frills excursions..don't think they've got their 2008 programme up yet..but here's a link
http://www.nofrills-excursions.com/principal/index.php
for something a bit different, try the old Mallorcan farmhouse, la Granja.
http://www.mallorcaweb.com/reports/manor-houses/la-granja-in-esporles/
There is another old place here, Es Calderers
http://www.elscalderers.com/home/default.aspx
or there's La Reserva, a nature reserve and walk, with a BBQ at the end
http://www.lareservaaventur.com/
Not sure if you can get excurions to these last three nowadays, we've been by coach in the past.....but if you're hiring a car they are certainly different.......