Manatees are very soothing animals. They're big and squishy and they spend their days floating around eating seaweed and giving each other slow head bobs of recognition as they pass. They would give great hugs, and you could totally hug one whenever you wanted because they're a) herbivores, b) pacifists, and c) really slow. They are basically the animal equivalent of a meditation tape, without all the hippie woo-woo associations or the staggering boredom.
Bonus fact about manatees: members of the Manatee Fan Club are called Fanatees. Benefits include a shiny lapel pin and a quarterly newsletter in which manatees teach you how to relaaaax, man, because everything is going to be just fine.