Is there something encoded within us that makes us attracted to, e.g., someone
- taller or shorter
- with blonde or brunette hair
- with green or blue eyes?
Or, is this phenomenon completely based on our social/cultural environment?
Yes, there is a biological basis. Your examples seem a little social/cultural to me, though. In any case, here are some examples I came across. One study that showed that women's hormones rose in response to smelling male sweat. There's also a large psychological component that, for example, shows people find symmetry important in beauty.
A review discusses various aspects of facial beauty, and mentions that several studies have shown certain physical attractiveness standards are common across ethnic groups. It also mentions another study that shows how women are more attracted to a "masculine" face during the high-risk phase of their menstrual cycle.