I am going to be staying in Ennis for 1 night in August. I'll have the next morning to fish until about noon or 1. I'm staying at the little cabins right on the river at the bridge in Ennis. I've never been there before. I'll have a 5 weight in hand.

Do I have a chance?

What's the best approach?

Any info would be greatly appreciated.

Valley garden can be very good,and O'Dell also. There is a great campground on the river and it's fairly cheap at about $5. Beetles, ants, and any caddis that is hatching.
The previous post about the veracity of the Ennis fly shop is correct: good, honest info.

You can walk a hundred yards from the cabin and be fishing, and cabins are wonderful.

Perfect guys thanks a million.

My family and I are making a road trip to Jamestown ND of all places (visit wife's brother and his new bride) but I told the wife that I refuse to drive through Montana in August unless I can get out on a river and fish at least half a day.

My oldest daughter's name is Madison so the Madison River seemed like a fun way to keep the family involved. We can get pictures of road signs and such and then head down into Yellowstone for the afternoon.

I will get some time on the Yellowstone River on the return trip as well.

Lots of choices to pick from. Ennis is some of my old stomping grounds. You might investigate the "canyon" area below the dam on Ennis Lake. It's been a long time since I was there but the browns and rainbows use to be stacked in the pools there. But watch where you put your hands. There's some badass snakes in that area. I've only fished it during the elk season and never in August. The water might be a tad low in August. Too much good water in that area to do much in half a day...... If you have the money, look into fishing Odell Creek. It's private and the browns (all wild) will average over five pounds.