There's nowhere to stay in the construction area. The problem will be getting from one side of it to the other. Basically, it won't be possible to get to the Lamar country from West Yellowstone after the 16th of August, and won't be possible to day trip from Gardiner to Old Faithful (or the Firehole or Madison, really only matters after about Sept 25 for me). The big thing is making sure you're staying where you can actually get to what you want to fish. Coming up dreaming of Slough Creek on 8/25 and staying in West Yellowstone will be a HUGGGEEEEE disappointment.

And what's this about fishing in close proximity to others??? I never do it unless my clients insist on fishing Soda Butte. I usually see fewer than five anglers on my trips, and often I (or my clients and I) are it. You just have to leg it or be willing to canyoneer.