You did good waiting, because used car prices definitely seem to be falling and I think that will continue. Also, renting a car away from the airport is a pain. You've paid your carless dues, and I certainly agree with you that you deserve to have a car accessible as you need it at this point!
Now I'm going to go an alternative route and make a suggestion that may sound absolutely crazy to you and everyone on this board, but I've done it twice and been very happy with the outcome both times.
The first step is figuring out what you want. You are already doing that. Go to lots and kick the tires, sit in a bunch of cars to see how comfortable you are, etc. During this time, I highly advise going on the website Autotrader.com, which carries pretty much all used inventory that is at dealerships as well as a bunch of vehicles from private sellers. This is waaaay more legit than Craigslist or Facebook marketplace. Browse online at Autotrader with parameters that make sense to you. You can limit the years or the mileage. Once you've picked a make and model, it will pull up a list with options. Change the "location" from 50 mile radius, which I believe is the default, to "nationwide." Sort by price - lowest. Ignore sponsored results.
Pick additional things you care about. I'm picky about colors. For example, I don't like white exteriors (although they are very popular) and I don't like black interiors (too hot, but again this seems to be the most common color). So I select all the other colors and refine my search. You may love a white car with a black interior, but it's up to you. Eventually, with some poking around on Autotrader: Ta da! Your perfect car!
Your perfect car is probably available in multiple places, but some places have much lower prices or certain types of cars than others. Figure out where that is for your perfect car. For example, when someone in my family wanted a full size pick up truck of a certain make/model/trim, he figured out that at that moment in time they were WAY, WAY cheaper in the NYC area. Like $8000 less for identical used trucks that we can get where I live. So he rank-ordered his top six in the NYC area, I bought plane tickets for the next morning, and we flew one way to NYC, rented a car, and then started on the list. We bought the second one we test drove, stayed the night at a Hilton while the dealership sorted the paperwork, and the next day I turned in the rental at a convenient branch location (not where I picked it up), and we drove home. The trip cost us less than $500 including gas, car rental, and the hotel. It was fun!
I did it again two different times to buy luxury cars in rural Georgia. Turns out trucks are very expensive in rural Georgia, but that one weird ultra-rich guy is having trouble finding a buyer for his used <insert ridiculously expensive car brand> here. In one of those transactions I was trading in a car (we negotiated the trade in value and purchase price prior to the trip, all dealerships should be able to do both remotely now.) Since I was buying more of a unicorn car rather than a shopping a ranked-list and all the negotiation was prior to my departure on the shopping trip, I used a cashier's check made out for the agreed amount. One of the transactions took two trips: one to kick the tires and be sure we wanted the car (and for the seller to agree we would were acceptable buyers, lol), and two to actually take the cashier's check and pick it up.
I realize at this point I probably sound crazy, but I do not regret any of these purchases. In all cases the end result was awesome, and I enjoyed the trips and the process. Driving a new-to-me car home is fun.
In any case when you go to a dealership, they are obviously going to try to sell you what they have. It may or may not be what you want. Bait and switch on advertisements is unfortunately sometimes a thing as you are finding. So call and make appointments on a specific car of interest if you are doing the travel to buy route. Or you will pick a car you do want to buy and then they will try to upsell you an extended warranty, "insurance", security system, rust proofing, whatever. Just make a life philosophy right now that you absolutely don't want those upsales things on the day of your car purchase. When they put on the heavy sales pressure (and they will), stick with the mantra "sorry, I have a life philosophy against that type of thing." You don't have to explain why. Feel welcome to walk away if they are really a jerk about it. Because there is literally always another car.
It's okay to tell the local sales guy a the local place "please keep an eye out for XYZ car and call me" if they don't have what you want. But, don't let them push you into something that isn't what you want, isn't in great shape, or isn't a really good deal. Finally, I will let you know that an Avalon is super nice to drive, but they are longer and much more difficult to park than a corolla or prius, for example. Since you may be parallel parking, this is something to consider.