Now have hiked all of this country and you can't go wrong. Have been off and on back in this Thorofare country since 1982. Glad that you are wanting to stay at 6C2 for this is a favorite place of mine also. A couple of other favorites of mine are also 6Y6 with right on the Yellowstone River. Here there is a nice bluff nearby that has outstanding views. Also 6T2 is a nice site in the trees near the Thorofare River. Near this site some years ago was a Wolf Den and numerous times would see the wolves back in here in the area. Site 6T1 is okay but the last times I was there, every spring during runoff the Thorofare River erodes the bank bigtime here in the are so do not know how it is now. Yes lots of the sites along the lake are wonderful. But love the Park Point site at 5E9. Also once back in here one of my most favorite spots is the confluence where the Thorofare and the Yellowstone Rivers meet - it is nice place. Also plus the whole Yellowstone River bank can be walked, all off trail, between the confluence and the 6Y6 campsite area. Have done this many a time and it is truly a special wild experience. No telling what one may encounter back in here.
And you are gonna go all the way to Brooks Lake ... Good for You! Now could give you a bunch of special tidbits. But of course you will go by Bridger Lake - Hawks Rest, which is nice. I would really recommend going up to Younts Peak at the very head of the Yellowstone. Fabulous Place!!! Climb the peak if you can for a terrific view. Be on the lookout for there are always some Grizzlies near Younts Peak for it is a cutworm moth site. I have seen bunches of Grizzlies in this area thru the years. There is a trail up the South Fork of the Yellowstone which is doable. Nearby is the North Fork of the Yellowstone, offtrail but really scenic. Now it is an easy traverse across the Buffalo Plateau and highly scenic. Lots and lots of good country in here where one could get lost on purpose all summer and never once have a bad day.
If you have any questions then feel free to me a message. Good for you and Wishing You the Best on this.