Hertz might be what you are looking for. With 20-30 rentals a year, you'd have a psuedo-elite level called Five Star within the #1 Club Gold program, and that seems to earn quite a few upgrades. 40 rentals gets you President's Circle status, which yields a lot of upgrades.

For longer rentals, you could earn #1 Awards points which are actually quite valuable - 600 points = 1 Free Day, no strings attached and very few blackout dates. For short rentals, you could opt for Marriott Rewards points or #1 Awards points, or miles in a few programs.

Finally, Hertz seems to be more consistent at its off-airport locations than other companies. Even in places where they don't have any kind of Gold desk, they do recognize the status and make sure you either get an upgrade or at least get a nice car within class. (A very small location might not have any premium cars to give you.) Importantly: the process of renting from Hertz downtown locations doesn't change. Contrast that to some other companies, where paperwork and odd an inefficient processes might be used at small locations.