Your profile location is Alabama. I'm from north central Alabama.
I find all of my stuff near small creeks. There is a cave on the most productive creek in somebody's backyard (unfortunately). There could very well be a higher density of artifacts near your cave, but you can find them anywhere on the river (provided its a natural waterway.) Look for scraped areas near the river, like logging trails, power lines, fields. If you have these areas near the river, you have a good chance of finding artifacts. If you have a logging trail or power line running parallel to the water, that is great. I have both of those near my best creek and stuff washes out of the bank after every good rain. Often I find arrowheads in the middle of the trail that weren't there the day before. It always amazes me.
I wouldn't necessarily pay any greater attention to areas that are known Indian camps. I would search every scraped area near the river that I could find, over and over. If its a natural body of water there are going to be artifacts. If you can get to areas near the river that are isolated and hunted very little, most likely the hunting is going to be better than any known site near a cave.
Hunt any smaller creeks, and even ditches, than run into the river. The best places are going to be where two or more waters converge.
The most productive areas are going to be higher, relatively flat areas near the water and the eroded areas that wash from the high spots. The higher areas don't have to be very high, just high enough not to worry about floods.
If your river is like my creeks, its going to be very hard to search the actual water. My creeks have sedimentary material, muck, mud, and sand. Vegetation grows all the way to the water and covers most of the bank. Snakes , mosquitoes, ticks and poison oak infest the water in the summer when the creeks get shallow enough to walk.
The hardest part of learning to hunt is training your eye. Once you accomplish that, finding stuff is pretty easy.
I created a Squidoo site earlier this year that should help the beginner get started, especially one in Alabama. I've only been seriously hunting since last October, so I can relate to beginner wanting to find things, but not quite knowing how to start.
http://www.squidoo.com/huntingarrowheads
I'm temporarily living in Colorado right now. I'm going to have to learn how and where to hunt here. I can already see that hunting here is a lot different than Alabama.