I'm looking for a word that describes a curious, interested state of mind- open minded, exploring, wondering, but without being nosy.
"inquisitiveness" and "inquiringness."
inquisitive: given to inquiry, research, or asking questions; eager for knowledge; intellectually curious: an inquisitive mind.
inquiring: seeking facts, information, or knowledge: an inquiring mind.
Alternately, consider "thirst," "craving," "appetency,"appetite" (for learning, knowledge, etc.), and "intellectual acquisitiveness."
acquisitiveness: having a strong desire to acquire things, as ideas and information: an acquisitive mind.