I can't say that I have too many challenges being car-free, since I've been so for the 34 years I've been on this planet (no comments on previous planets!). I do want to contribute something ON TOPIC to this forum, so here is a thread calling for car-free folk to discuss specific challenges of being car-free, and the solutions they found for those challenges. And if you are still looking for a solution to a challenge, someone else may have a solution for you.
Challenge #1: Pets and the vet. How do you get your pets to a vet without a car? Possible solutions available to me (and hopefully some of these are to you as well):
1- Call your cab company, they may allow small animals in carriers. We can take cats in our cabs.
2- Call animal hospitals, some offer a home visit service. The extra cost may be worthwhile compared to travel costs.
3- See if you can bring multiple pets in at the same time for annual exams, saving travel hassle. As a bonus, our vet gives a discount for group visits.
4- Look for a pet taxi service in your city.
5- A 30 minute walk is basic daily exercise for your dog - next time you move, look for a place within a 30 minute walk of an animal hospital.
6- Consider only getting pets light enough to carry for a long distance. You can walk around with a Chihuahua in a chest carrier for hours... but don't try that with a St. Bernard!
7- Train your dog to be comfortable in a carrier towed in a bike trailer, or get a dog-specific trailer.
Anyone else want to contribute solutions to the challenges of being car-free?