Depending on the flexibility of the "not crowded" stipulation, I'd recommend one of the bigger national parks that have shuttle service; I adore Zion NP in Utah but lots of parks have been implementing shuttles so I don't know what the complete list is at this point...but that would let you stay in the park hotel, have the general store right nearby, probably a few trails right there plus whatever the shuttle can take you to. Note: I've only been to Zion in April & May, it might be blisteringly hot in September. A lot of parks in the southwest may be worth avoiding on that basis, e.g. Grand Canyon.
Another thing to consider is out-of-season ski resorts. My dad's academic field loves to hold conferences at ski resorts in the summer, and he took us along a few times. Aspen (CO) definitely had some trails right off the lodging area, and it was beautiful. However, it does double as a mountain biking resort in the summer (they use the lifts for the bikers!), so demand isn't quite rock-bottom; but it does mean some amenities like groceries might be open that otherwise wouldn't? Protip: at ski areas you can rent a small condo instead of a hotel room so you can cook comfortably.
Or get your wife to woman up and hike out to a secluded lake! Skinnydipping and any bush you choose to pee behind is completely your own! ;) [I'm pretty to-each-their-own...but women refusing to go camping feels to me like a betrayal of the Sisterhood. Reinforcing stereotypes and all that.]