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The Bible repeatedly refers to honey as a good thing – for example, the land promised to the Israelites is regularly referred to as "a land flowing with milk and honey" (e.g., Exodus 3:8). But in such cases honey is more clearly a reference to wealth or sweetness, not necessarily physical healing.
The clearest connection between honey and physical healing is probably in Proverbs 16:24:
Gracious words are like a honeycomb, sweetness to the soul and health to the body. (ESV)
More frequently, honey is sustenance that physically benefits people. For example, Jonathan's "eyes became bright" after eating honey in 1 Samuel 14:24–30. Honey also sustains people in passages like Deuteronomy 32:13, 2 Samuel 17:29, Psalm 81:16, Ezekiel 16:13, and Matthew 3:4.
On the other hand, eating too much is warned against in Proverbs 25:16:
If you have found honey, eat only enough for you, lest you have your fill of it and vomit it.
A complete list of references to honey in the Bible can be found by using a concordance, or an online tool like Bible Gateway.