ANSWER: There are at least twenty-two places in the Bible (King James' Old Testament) where the word DRAGONS (or its singular form) are found. Some of these are Deuteronomy 32:33, Nehemiah 2:13, Psalm 44:19, 91:13, Isaiah 13:22, 27:1, 43:20, 51:9, Jeremiah 49:33, 51:34, Ezekiel 29:3 and Malachi 1:3.
The vast majority of Old Testament references to dragons are derived come the word tanniym (Strong's Concordance #H8577). This Hebrew word can literally mean a jackal, serpent, crocodile, or even a whale. This same word was used for Moses' rod that became a snake before Egypt’s Pharaoh (Exodus 7:8 - 9).In Isaiah 34:13, 35:7 and 43:20 the original language word used is tan (Strong's #H8565), which can mean a sea serpent or other very large sea animal. Probably the closes thing that resembles the beast we imagine is in Biblical references like Psalm 74:14 where it discusses a huge beast called a Leviathan.
Let us now tackle your question about Jerusalem having a well for dragons. Nehemiah was a prophet held captive by the Persian Empire. He was released and given permission to return to Judah and rebuild Jerusalem and its walls. After arriving in the city, he toured the walls to assess their condition before reconstructing them. On his journey, he mentions something rather odd.
"And I went out by night by the gate of the valley, EVEN BEFORE THE DRAGON WELL. . ." (Nehemiah 2:13, KJV)
What do we know about this well? The New Interpreter's Commentary thinks it could be another name for the natural spring named En-rogel mentioned in 1Kings 1:9.
The International Standard Encyclopedia thinks it was a well dug in this area. An alternative name for this particular well is jackal's well, a translation found in the New American Standard and New International Version translations. The Hebrew word translated "dragon" in Nehemiah 2:13 is tanniym (which we mentioned above).
The King James Bible translation referring to a well for dragons is indeed colorful, but somewhat misleading in modern English. If "tanniym" does not mean "jackal" here, it probably then refers to a snake rather than some large legendary or mythological monster. Thank you for your question.