The use of mate on it's own implies more than just sex, so this question will take some thought. I have had very few "mates" in my thousand years, but they all seem to have a few common threads.
I desire someone strong and independent, who is not needy or overbearing. At the same time, I want someone who needs me and who I can care for and protect. I need someone of intelligence, who I can carry on a civilized conversation with. A lack of depth is incredibly off putting. I desire someone who compliments me, both aesthetically and mentally, someone trustworthy and loyal, someone I can rely upon and who will not judge me. I look for someone who challenges me and fascinates me so I do not grow bored too quickly.
Also, they pretty much must be blonde. I seriously adore me some blondes.