David, I'm responding here because others might find it useful.
For the most part, you can't go wrong with this trip. There's something interesting in every mile, and each backcountry site seems to have a virtue. That said, what follows are a few suggestions:
-For passionate fly fishers, be sure to spend chunks of time in both the lower Bechler and upper Bechler. Different trout, very different rivers. The lower is meandering and slow, with deep holes and extensive snags and big rainbows. Those fish were quite wary and I got best results from full stalking shenanigans (crawling to the edge of the bank, etc). The fish in the fast upper are smaller, but live in tiny pockets and strike hard and fast. Fishing both in one day was great.
-Bring lots of flies. I almost ran out.
-Do not miss the Mr. Bubbles hot spring. 9D1 gives you easy evening access.
-I'd highly recommend a side trip to Shoshone Geyser basin. Even if you don't stay there, you can hang your gear at 8G1 for easy day hiking. The fish in Shoshone Creek aren't big, but if you like small creek fishing I'd recommend devoting some time to it.
-The Firehole around Lone Star geyser gets a fair bit of pressure, but they bite and if you have the time to wait around seeing it erupt is pretty cool. You'll have enough warning from the sputtering to stop fishing and come back to watch if you stay in sight.
-I like staying in the old/original part of the Old Faithful Inn. If you call them directly you can request specific rooms. Make reservations early. I like anything in the 150s. Those rooms do not have a contained bathroom, you'll have to walk down the hall. Do not eat dinner at the Inn. The restaurant at the Snow Lodge is much, much better and only marginally more expensive. Breakfast at the Inn is ok.