If you visit the New York State Museum in Albany, you will see the Cohoes Mastodon.
The mastodon was discovered in September, 1866 during the construction of Harmony Mill #3 (one of the largest cotton mills in the world) near Cohoes Falls on the Mohawk River. Here's the sign on North Mohawk Street, at the northwest end of the massive Harmony Mill building (now apartments).
The bones were found buried in a deep pothole at the base of the falls. The falls themselves can be viewed from the appropriately named Falls View Park in Cohoes.
The potholes formed during higher water flow just after the last ice age. As the glaciers still sat up in Canada, the massive volumes of fresh meltwater created Glacial Lake Iroquois where the smaller Lake Ontario sits today. This water ripped through the Mohawk Valley into the Hudson Valley with 100 times the water flow of today's river.
Based on growth rings in the mastodon's tusk, we can determine he was around 32 years old when he died some 13,000 years ago. He led a hard life, almost starving to death at 11 from a wound to his lower jaw (probably from the tusk of another mastodon) and dying at 32 from another tusk wound to the temple. Here's a neat video from Dr. Robert Feranec at the New York State Museum talking about the mastodon.
The Cohoes Mastodon display at the State Museum is well worth visiting with a lot of information presented about this mastodon and mastodons in general. Around the corner is also the famous mastodon diorama recreating a mother and baby mastodon in the mid-Hudson Valley with Storm King Mountain in the distance.
These were real animals literally walking around our backyards a few thousand years ago.