
Image of "Dr. How's Electric Incubator" from 1903 similar to the ones in Atlantic City. From Library of Congress.
The first incubated babies in Atlantic City appeared on Young’s Pier in 1904. According to a New York Times article written the same year, “the ‘scientific mother’ as the incubator [had] been termed, [was] caring for seven babies.” The author also noted that “all the little tots [were] gaining strength.”
The babies were quickly a big hit. In a publication from 1908, author Gaston Lichenstein praised the exhibit, stating that “Young’s Pier offers the intellectual tourist more interesting attractions than any other…to be observed on the various piers and the famous Boardwalk.” Of these “interesting attractions” Lichenstein gushed about were the incubator babies which visitors could see for a mere quarter. Below is an excerpt from his book, A Visit To Young’s Pier Atlantic City, N.J., describing the incubators:
Four babies are being cared for by the institution on Young’s Pier. One of them, a healthy youngster of eleven pounds and four ounces, arrived on April 15th, weighing three pounds and two ounces. He is a seven months’ premature specimen. Another, that arrived on April 20th, weighing two bounds and twelve ounces, now tips the scales at eight pounds and eight ounces.
A Filipino premature baby of six months, the smallest baby on record in the world that is alive today (June 26, 1905), is twenty six days old, and weights two pounds and two ounces.
Only nature food is supplied, and the different babies are subjected to varying temperatures, from eight-five degrees upward, according to their condition.
A scale, weighing to a small fraction of an ounce, is publicly exhibited. This delicate apparatus insures accuracy. The “nursery” is enclosed in glass, so that visitors can obtain a full view of the artificial arrangements.
Three of the four infants came under my observation. The extraordinarily youthful Filipino, who is yet imperfectly developed, lies in a state of apparent obliviousness, but, a youngster about to be discharged, who now lives in the open air and who was being held by a nurse, appeared strong and healthy like any normal child. (A Visit to Young’s Pier, 4)

The Boardwalk at the turn of the century. In the background, Young's Pier, where the incubator babies made their debut. From Library of Congress.
Interesting Tidbits:
On Sept. 16, 1916, The Washington Post ran an article about a Mrs. Richard Elkins who adopted a “war orphan” baby from the incubators. The baby, whose father died in WWI and mother not long after giving birth, caught the eye of Mrs. Elkins. “A frequent visitor to the incubators, [she] became deeply interested in the ‘war orphan’ with the fascinating smile.” The grandmother of the baby consented to its adoption by Mrs. Elkins who then had a priest sent to the incubators to baptize the infant.
On July 5th 1927, a fire swept through Atlantic City supposedly started by a lit cigarette carelessly thrown on the Boardwalk planks. Before the flames could be tamed, they had scorched nearly a city block on the Boardwalk between Columbia Place and Arkansas Avenue. An article from the New York Times reported that “about fourteen babies were in an incubator building on the Boardwalk, one of the places destroyed [by fire].” However, the babies in peril were rescued by physicians, nurses and good Samaritans and carted to shelter within the Shelbourne Hotel.

Display ad from The Washington Post in 1901 describing "a curiosity of advanced civilization" and promoting "Dr. Pierce's Favorite Prescription."
Sources:
Gason Lichenstein. A Visit to Young’s Pier at Atlantic City, N.J.: Also, When Edgecomb Was a ... - Gaston Lichtenstein - Google Books. Richmond, VA: WM Ellis Jones, 1908. http://books.google.com/books?id=EnItAAAAYAAJ&pg=PA3&dq=Young%27s+Pier+incubator&hl=en&sa=X&ei=NWjJUMeVL8rg2AWKtoH4DA&ved=0CDAQ6AEwAA#v=onepage&q=Young%27s%20Pier%20incubator&f=false.
Special to The, Washington Post. 1916. Adopts "war orphan". The Washington Post (1877-1922), Sep 19, 1916. http://ezproxy.lib.utexas.edu/login?url=http://search.proquest.com/docview/145464247?accountid=7118 (accessed December 13, 2012).
Special to The New,York Times. 1927. Atlantic city fire lays block in ruins. New York Times (1923-Current file), Jul 06, 1927. http://ezproxy.lib.utexas.edu/login?url=http://search.proquest.com/docview/104118611?accountid=7118 (accessed December 13, 2012).
Display ad 23 -- no title. 1901. The Washington Post (1877-1922), Jul 02, 1901. http://ezproxy.lib.utexas.edu/login?url=http://search.proquest.com/docview/144251968?accountid=7118 (accessed December 13, 2012).