You could buy an experience at www.dubaiautodrome.com. The single seater experience looks like fun.
Have a look at the offer/voucher sites for massages etc .
A meal out. Time Out had some fabulous vouchers in last weeks edition, choose from a restaurant in there.
Arabian Ranches Golf Club has a Fathers Day meal planned I am sure other places do to.
An IOU foot massage, lie in, designated driver etc etc.
Also take a look at expatechodubai they have some ideas on their web page.
It depends on your budget and location for some of the above.
<em>edited by Queen Bee on 14/06/2011</em>
I've been searching since like two or more weeks but nothing. there are plenty of places but it seems that in this place they don't bother celebrating it!!! I don't know. I sent couple of emails especially to the Dubai mall but they never reply