I drove my Jeep over the border a couple of weekends ago, from Atlanta to Mexico City.
Lots of Mexico is accessible via highways these days (usually gotta pay a toll though), and I find driving on them much more enjoyable than in the US. The semi trucks actually wait for you to pass before trying to pass another vehicle themselves, so I used cruise control almost nearly uninterrupted the entire trip.
Re: rural areas, I've driven through wine country in Baja California and through farmland in CDMX to get to the volcanos (both via dirt roads), and never had issues. I'd just be very mindful of the topes that are scattered throughout Mexico like landmines. You won't find them on highways, but you'll usually find them on city/town streets, and they're usually unmarked. I think it's one of the reasons why people recommend to not drive at night if you're unfamiliar with the area.
Parking in the city is fine. I've seen really nice cars (Mercedes, Tesla, etc.) parked along the streets, but there's generally paid secured parking if you're uncomfortable with leaving the car on the street.
All in all, I'd say it's been an enjoyable experience. Know the driving rules in the major cities that you plan to drive through (foreigners can't drive on Saturdays in CDMX), and you should be fine.
You're more than welcome to ask me additional questions if you'd like!