"Takes a flyer" basically means to take a risk or gamble on something. The opposite or antonym of "taking a flyer" would be to play it safe, to avoid risks and not take chances. Other antonyms of "takes a flyer" can be cautious, prudent, or level-headed. These words implies careful consideration and thought before making any decision or action. In essence, the antonyms of "takes a flyer" suggest a more measured and thoughtful approach to decision-making, whereas "takes a flyer" implies a more impulsive and bold approach. Ultimately, the best approach may depend on the situation at hand and the risks and rewards involved.