One interesting source for this is Dutchman Adriaen van der Donck's 1655 first-hand account Beschryvinge van Nieuw-Nederlant (translated in 2008 by D.W. Goedhuys as A Description of New Netherland). In it he gives descriptions of the geographical, botanical, zoological and ethnological aspects of the New Netherland colony on the East Coast. Among it, there are descriptions of the large fauna (mostly real) known to him. He does not mention how noteworthy he finds them (to me, he seems more interested in their economic value), but his observations are interesting regardless.

Lions are the first he mentions, although he notes that they are never seen by Christians. The pelts of females were rarely traded by the natives, who reported they originated from far to the southeast and that the males were too quick and dangerous to hunt. I can only assume he is talking about cougars.

Bears are mentioned to be plenty. Van der Donck notes the differences with the bears from Muscovy and Greenland, namely that the ones in New Netherland ones are shiny and black. They are noted to be rarely spotted by Europeans, because of their keen sense of smell (the bear's, not the European's) combined with their shyness. Curiously, he ascribes to them the ability for pressing gunshot wounds with wads of leaves, after which they will rush to the origin of the shot to attack. Hunters are advised to keep a thick tree with lots of branches nearby to hide in (or to shoot from a second time) if the shot fails to kill. They're not considered dangerous if they're not attacked. Another difference with the previously known bears is their diet of grass, herbs and nuts. Their fat was eaten by the natives and some Europeans and considered very nutritious and tasty. Also good for making muffs, apparently.

Buffalo (oddly called "Eeland" in the original, Dutch for elk/moose), which generally stay away from humans, are especially noted for their possible potential as working animals and possible cross-breeding with Dutch cows, as well as their excellent meat. Van der Donck mentions that there have been specimens that were raised from their youth and were succesfully tamed. Good for making vests.

Despite being hunted in great numbers by the natives and by wolves, deer are very numerous, both white and black ones. Van der Donck is sceptical about the natives' report that the white ones attract more other deer than the black ones.

He has heard talk from a Jesuit about "forest oxen" in Canada, Boves Silvestres, the size of a horse, with a neck like a camel, covered in long hair like a horse's mane, a short tail and cloven hooves. Moose?

Mohawk (called Macquase by Van der Donck) have told him of a rare horselike animal, with cloven hooves and a single horn, living further inland. He has never seen any, but he chooses to believe the native hunters, as well as the Europeans who have seen the skins (but not the horns).

Wolves are also common, but are noted to be smaller and less fierce than those in the Netherlands.

After that, he only mentions smaller animals, including the beaver, to which he dedicates an entire chapter.

Keep in mind that this is the report of only a single European settler. Someone else may be able to give a more general idea of their views.

Also, because I love the book, if you want to read more about the New Netherland colony and Adriaen van der Donck's role in it, I would like to recommend Russell Shorto's The Island at the Center of the World.