My mom and I visited this park for a day trip in late June, 2013. The 3,000+ acre park is worth a visit, and my guess is that it would be fantastic for the fall colors. Nature was the star of this show, since many of the park buildings were closed during the week. Prepare for steep trails and lots of beautiful scenery.
The cave is not a cave, but a cliff with an overhang. The climb to see them is steep, but it's worth it. Vandalism has ruined many of the hieroglyphics; still, it's easy to imagine Native Americans living here. See the official site at:
http://outdoornebraska.ne.gov/nebland/articles/parks/indiancave.asp

Steps leading to the "cave"

Steps leading to the "cave"

It's quite a climb and not wheelchair accessible

It's quite a climb and not wheelchair accessible

Steps!

Steps!

Unfortunately, many people carved their names among the hieroglyphics

Unfortunately, many people carved their names among the hieroglyphics

Getting closer to the carvings

Getting closer to the carvings

The walls were steep and high

The walls were steep and high

Textures were fantastic!

Textures were fantastic!

One of the few original carvings I could find

One of the few original carvings I could find

Great textures in stone!

Great textures in stone!

Wildflowers were abundant

Wildflowers were abundant

Wild raspberries were my mom's favorite part of the trip!

Wild raspberries were my mom's favorite part of the trip!

Hiking trails were steep and challenging

Hiking trails were steep and challenging

The Missouri River overlook was a great place to have lunch.

The Missouri River overlook was a great place to have lunch.

It must be fantastic at sunrise!

It must be fantastic at sunrise!

Roads and trails were heavily forested

Roads and trails were heavily forested

Picnic areas and tent camping were abundant

Picnic areas and tent camping were abundant

Fantastic Scenery

Fantastic Scenery

Hardwood forest

Hardwood forest

Wild Roses

Wild Roses

Raspberries were ripening!

Raspberries were ripening!