There's no quantifiable set of criteria for what anyone of either gender is actually looking for in a partner of either gender - like people themselves, wants and needs and requirements are all over the map. Some women, for instance, have an idealized view of what relationships should be like (built up from what movies, TV, and other sources tell them they should be like) which may or may not have a bearing on reality. Women are hardly alone in that category, though; men can and often do have preconceptions about what relationships should be like that may not match up with reality. Once you get past that hurdle, you also need to deal with disparities between the people involved - how much attention they need/want, how much intimacy, and a hundred other factors that figure into any relationship.
For me personally, I primarily look for intelligence and an appreciation for the abstract in potential relationships - not to say physical attraction is unimportant, but it takes a back seat to my desire for a potential match to be an intellectual equal and capable of keeping up in a discussion about esoteric stuff. Shared passions, hobbies, and general outlook on life are also helpful. This is an evolution on the criteria I had when I was a younger man, which emphasized physical attraction much more - I had a naive willingness to settle for less of a match in the intelligence/personality area if the initial physical attraction was stronger. It's a somewhat common issue for younger men, and one that often leads to disinterest in the relationship once that early-stage ardor dies down into the steady smolder of routine.
Long story short everyone has to find another person that's a suitable match for them - someone who can meet them in the areas they deem important to them.