I've been advised that since I'm traveling midweek and would need to be back at the airport by about 5:30pm it's not a good idea to leave. So the question is which terminal is best to hang out in between a european and west coast flight? Any place to get fresh air? (why, oh why don't they design airports with public gardens?!?) I arrive in terminal 8 and depart from 9.

These I believe are both American Airlines terminals. If you leave either terminal to go outside and get air, you will have to be re-screened for security which depending on time of day, may take awhile. Otherwise, there are no internal areas to get some air.

Terminal 8 houses a selection of fast food dining options such as McDonald's, Nathan's (great fries there), Wok & Roll, Edy's Ice Cream, Everything Yogurt, and Broadway Brewing to name a few. There's also a shop there that sells New York City souvenirs. Over in Terminal 9 there's a DC retailer, a bookstore, and Brookstone which is a good store for browsing through their unique gadgets, Food choices are Sbarro's for pizza and Italian, Starbuck's, Au Bon Pain, a TGI Friday's (chain), and 2 others whose names I can't remember right now. I agree with you that it would be nice if there were some sort of pretty garden area to rest in at airports. As Lmaev pointed out getting fresh air will mean be re-screened for security. Maybe you could walk around and browse, have a drink, food, etc. and people watch.

Would it make sense to try to get yourself a cheap airport hotel room with a TV, like on Priceline? Then accumulate a bag of food & drink and lie around in an air-conditioned room & watch TV, doze, take baths, etc. That is proably what I would do, at any time of day, but I am lazy & also can't sleep on a plane only in a bed.

Why not buy a day pass to AA Admirals Club. I believe it's $50. The international terminal one is better, but both are a nice peaceful way to kill few hours. Many TVs, magazines, newspapers, cash bar, comfortable couches ,quiet little corners everywhere, if you have a wireless set-up on your laptop the AC is set-up for that as well. But for me it's the quiet, relaxed atmosphere in the club that makes it nice. They also have private shower rooms, which could make the wait and the following flight so much better. Anyway I don't have to pay for it, so I'm not sure if that is something that's worth $50 to you, but it's a thought.
Have a great trip!

I should have also told you that if you are flying AA from one of the major airports in Europe, you could buy the day pass there and use the AC before the transatlantic flight as well. The pass is good for 24 hours for any AC clubs.
The nice additional feature of the European ACs is that they have a self serve free bar, and it is stocked very nicely with above average brands, as well as good wines and beers and snacks.