The phrase "turn up one's nose" refers to a disdainful or snobbish attitude towards something. While there are no direct antonyms for this phrase, some related terms that express a positive or more accepting attitude towards things include "open-minded," "non-judgmental," "curious," or "accepting." These terms suggest a willingness to try new things, explore alternative perspectives, and evaluate things on their own merits rather than based on preconceived notions or biases. By embracing these attitudes, we can broaden our horizons, increase our understanding, and connect with a wider range of people and experiences.