In looking at the local options, I found that Shoreline Flying Club, based at KPAO in Palo Alto, was my best option. They had a 1980 Cessna 182 (N5302N) on the line, have no monthly dues, an no initiation fee. Granted, the avionics are different, but the airplane and engine were virtually identical to the 1979 model that we'd purchased.

I scheduled several hours on both Sunday and Monday of last week to fly with William Hightower. When we first met, I explained my background and experience a bit, and then told him that my main concern was learning how to takeoff and land the 182. I reasoned that I could figure most everything else out along the way.
He agreed and we planned to fly on Sunday from Palo Alto airport down to Hollister airport so that I could get some practice on a big runway at a familiar and relatively quite airport. That'd let me focus on the airplane and not dealing with tons of other planes and/or controllers.
I spent most of the fight down there understanding how to trim the airplane and getting a sense of what it feels/sounds like at various power settings and whatnot. Down at the airport, we shot about seven full stop landings in the light crosswind on runway 31 before returning back to Palo Alto under a 1,500 foot cloud layer.
Much to my surprise, I was already fairly comfortable in the airplane after about 2.4 hours behind the controls.

On Monday we did basically the same thing, but we headed to South County airport instead. There we experimented more with landings in different flap settings--everything from zero flaps to the full 40 degree flaps (that was fun!). I also performed a simulated engine-out landing and a soft field takeoff. On the way home I got to play with the simple auto pilot a bit as well.
We ended the day with another 1.8 hours of time logged, enough to make me and the insurance company comfortable with my ability to keep from doing anything too stupid in the 182.
On both days, we did some other air work on the way to/from our destination. That included turns, stalls, slow flight, and the usual stuff one would expect in a new aircraft checkout.
Here are thoughts on a few specific aspects of the checkout that I was concerned about.