Darkness came down quickly, as they plodded slowly downhill and up again, until at last they saw lights twinkling some distance ahead.
Before them rose Bree-hill barring the way, a dark mass against misty stars; and under its western flank nestled a large village.
J.R.R. Tolkien, The Fellowship of the Ring, “Fog on the Barrow-downs“
In The Lord of the Rings: A Reader’s Companion, in an annotation for part of the quote above, Hammond & Scull point out that “Tolkien correctly makes no mention of the moon.”
The hobbits are traveling east on the road to Bree, and the thin waxing crescent moon would have set in the west within an hour or two after sunset, because (just like today in the real-world) this day is just a couple of days past the new moon (which also happened to coincide with Goldberry’s “washing day” and “autumn-cleaning”).
You can try to catch a glimpse of what this moon would have looked like tonight (September 19), as it sets with the sun, which should look almost exactly the same as depicted in the simulation below.
The Shire Reckoning Project 