I was watching an Esperanto video today and one of the subjects was using the accusative to omit prepositions. I am not familiar with this usage.

The host used this example (from a translation of the story of the pied piper):

"Iun tagon ŝalmisto vizitas la urbon."

It wasn't well-explained, so can someone explain this usage to me and provide a few more examples?

This is copied from Ivy Kellerman's A Complete Grammar of Esperanto. It's old but hopefully it's still valid and helpful.

LESSON XXI.

THE ACCUSATIVE OF TIME.

91. Duration of time and a date or point in time may be expressed
not only by use of the prepositions "dum", during, and "je", at, on,
but also (as in English) without the use of any preposition. When no
preposition is used, the word or words indicating time are put in the
accusative case:

Li restis tie la tutan semajnon (dum la tuta semajno),
he stayed there the whole week (during the whole week).
Sxi estis felicxa longan tempon (dum longa tempo),
she was happy a long time (during a long time; for a long time).
Ni rajdos tagon kaj nokton (dum tago kaj nokto),
we shall ride a day and a night (during a day and a night;
for a day and a night).
Mi venis dimancxon (je dimancxo), I came Sunday (on Sunday).
Tiun horon (je tiu horo), li forkuris,
that hour (at that hour) he escaped.

92. Although generally preferable, an accusative construction must
be carefully placed, or avoided altogether, if confusion with other
accusatives (expressing direction of motion, direct object, etc.) might
result:

Mi volas iri Bostonon je lundo, I wish to go to Boston on Monday.
Mi volas iri al Bostono lundon, I wish to go to Boston Monday.
Lundon mi volas iri Bostonon, Monday I wish to go to Boston.

ADVERBS AND THE ACCUSATIVE OF TIME.

93. An accusative of time, as well as a temporal adverb, may further
define or be defined by another expression of time:

Li venis longan tempon antaux tiu horo,
he came a long time before that hour.
Jaron post jaro ili restis tie,
year after year they stayed there.
hodiaux matene, this morning.
hodiaux vespere, this evening.
hodiaux nokte, tonight.
hieraux vespere, last evening.
hieraux nokte, last night.
dimancxon matene, Sunday morning.
lundon vespere, Monday evening.
mardon nokte, Tuesday night.

94. An accusative of time does not necessarily imply that the act or
state mentioned occurs oftener than the instance cited. An adverb from
the same root usually gives an idea of frequency or repetition:

Li iros al ilia domo dimancxon, he will go to their house Sunday.
Li iras al ilia domo dimancxe, he goes to their house Sundays.
Li laboris tagon kaj nokton, he worked a day and a night.
Li laboras tage kaj nokte,
he works day and night (by day and by night).

Thanks, that we helpful! I appreciate you providing that.

Speaking of older Esperanto textbooks on Gutenberg, I also found this one a little while back:

https://gutenberg.org/files/8177/8177-h/8177-h.htm

That place is a treasure trove.