The short: Native Americans lived across the entire North American continent, and therefore explored it, but general knowledge of any given group was probably more restricted to local regions since North America is huge and contained hundreds of different peoples, languages, and cultures. Many of the monuments we currently recognize in the U.S. were also valued by Native Americans, who wove those places into myths, stories, and religion.

The long: There are two correct answers to the first part of your question, and they contradict each other: Native Americans simultaneously completely explored the continent, and did not explore the vast majority of it (also, I'm going to write about North America here, since the examples you listed are from there). Millennia before the Columbian Exchange, Native Americans lived on all corners of North America, from Yukon to Florida to Baja California. So, as a whole, Native Americans knew of and explored all the places that we know to today (perhaps aside from physically reaching the highest peaks or most desolate deserts).

But, Native Americans were not one people, and they were spread across a vast area. North America is really, really big. Imagine living without planes, cars, trains, or even wheels. It would take years and years to travel around any significant portion of the continent, even by boat. So the indigenous peoples of the Hudson Bay probably had little to no conception of the American Southwest's deserts - along with being thousands of miles away from each other, these areas and peoples were separated by hundreds of different languages, cultures, and ethnicities. An average Iroquois individual in New York might know about Niagara Falls, but probably wouldn't have heard of the Rocky Mountains - just as a Swiss person in the Middle Ages might have known about the Matterhorn and not the Caspian Sea, which are a similar distance apart.

We have very little direct information about how much some Native Americans would have traveled, but its safe to say that some did, and often extensively. Many Native Americans were nomadic or semi-nomadic, and so would have known large areas well. And areas with high populations often had extensive trade networks which would have facilitated knowledge about distant regions. For example, we know that Native Americans at the Mississippian site of Cahokia, in western Illinois, were trading for goods coming from the Gulf Coast. Cultures in the Southwest traded with those in central Mexico. And many indigenous Mesoamerican societies had traditions of itinerant professional merchants (the Aztecs called them pochteca) who provide some of the best evidence we now have that some Native American individuals would have traveled widely.

Now, to the second half of your question. Many North American natural places' amazingness is only further proven by the fact that various Native Americans recognized the value of many of the same places that we do today. However, indigenous peoples didn't turn natural monuments into national parks; instead, we know Native Americans valued places like Monument Valley because they built myths and legends about them, and often identified them as sacred places. Mount Washington, the highest peak in the Northeast U.S., was considered a sacred home of the gods by the local Abenaki people, who didn't climb it in deference to that fact. Kiowa, Lakota, Cheyenne, and Sioux peoples all have legends about Devil's Tower, in Wyoming, which is now a National Monument. So, I would argue that it's safe to say Native Americans would have historically recognized the beauty of many of the U.S.'s current natural wonders - and modern Native Americans' stories and attitude towards national monuments (which also often contain their sacred lands) only continues that tradition.

Meta question: Can paleolithic inscriptions be used as references?