There was one time in my life when NOT having a car was perfect, and that was when I was in college. I could walk anywhere I needed to go on campus: to classes, the cafeteria, the gym, library, health clinic, and even a small convenience store for basic needs like laundry soap, tooth paste or a late snack. It was all within walking distance, and there was a campus shuttle if I needed an actual ride for some reason. Honestly, it would have taken longer to find a parking spot than to walk, so there was truly no need. I could always bum a ride for those rare occasions I needed to go off campus.
So I can imagine a life where having your own transportation is truly not a need. But for most people, I think having a car is pretty important. I guess it just depends on just how inconvenient your current transportation is. Would arriving at the bus stop 5-10 minutes earlier solve the problem of missing appointments? Or do you actually find yourself waiting 30 minutes or more for the bus, or taking huge detours that add 20 minutes or more to your trip? Because personally, that would be too much time spent hassling over rides. I guess that's how I'd determine whether it was worth it for ME to get a car. You may be more or less tolerant of waiting on buses.
Figure out how much room you have in your budget for a car. Consider not just how much the car costs (or the payments for it), but also the miles you typically drive in a week times the average cost of fuel, the cost of having auto insurance, the cost of registering a vehicle in your community, and the cost of both regular maintenance and unexpected repairs. Give yourself some wiggle room on all counts. Personally I would not get a fixer-upper unless you are mechanically inclined, because the cost of major repairs can easily add up to as much as you'd spend on a certified used vehicle, and they're usually unexpected and not easy to budget for. My husband fixes up old clunkers as a hobby, and I swear it costs more than the payments on our newer car some years. Good luck!