The museum has a large array of exhibits, explaining many of aspects of the ancient culture. I think they did a very good job. they are easy to understand, if you read English. If you don't, go to the Museum shop. There are guides in other languages there, for about a dollar, as I recall. Many other books and quality objects in the shop, too, for all ages and interest levels.
Just outside museum building are new paved walks to view the smaller mounds. You can walk around them easily, but aren't allowed to climb them. Obviously, that would do damage over time. Mounds have survived over a thousand years and it makes you think. Why did they get built? Inside the museum, you'll find those answers. Yet, no written language was left, so experts, and you, are really only conjecturing, right?
You can buy a booklet for your self-guided tour outside. Only a dollar in the shop. My brother got one & it was informative. Sometimes, they offer guided walks. Have any questions? You can ask me!
The main mound, not in photo, is where they believe The Chief resided. You can walk or drive up near it. A modern staircase has been build to climb to the top. The day we went, stairs were being repaired. We could only climb halfway up. From an earlier visit, I know we missed the grandeur of the experience. Walking around on the top is worth the climb, in my opinion.
The grounds at Cahokia Mounds are well-maintained, and there are several picnic areas. The mounds themselves are good habitat for native flora; I was there in the middle of the day, and I didn't see any fauna, but I imagine the critters come out either in early morning or at late evening.