I took your "hardy travelers" to mean you've been to Europe before. So I won't tell you you can't go to a major attraction on your arrival day. (I'll be really embarrassed if it turns out you meant "... in SUV Captain's Chairs, going to Six Flags.")
And while it's nicer to see the originals indoors, instead of the replicas left at Pompeii Scavi (and the erotica that's only in Naples!), I don't agree that the Archaeology Museum is even remotely as important as Pompeii Scavi itself. Opinion. I found the museum crowded, badly laid out (as in, flat display cases keeping you away from stuff on the wall behind them), badly lit, and hot.
Indeed, I suspect that many readers of this board completely overlooked the equally important Farnese Marbles, in the same museum. I would add that your departure from the US EAST coast is a big difference from a west coast departure. (Please fill in your home area in your public profile.) 2.5+ hours of door-to-door travel, each way from Rome, is an awful daytrip (to Pompeii.) And two days (does that mean one lousy night?) in Rome is way too little.
This board has so many first-time-to-Europe posters that it vigorously warns against driving on arrival day. But after fifty (50) trips to Europe, I can make my own decisions. (And I rarely drive, even later in the trip.) This is the first time, in many years, that I've heard the idea that one attraction or another is too important to see on arrival day from the US.
We found the sun and heat at Pompeii punishing, even in the last week of May. Our best investment was a Sorrento hotel with savage air conditioning. Yes, they sell water (and food) inside Pompeii, but no food inside Herculaneum. But you don't want to waste time in line for it.