My determinant factor, whether to have a car or not at my externships is first to figure out how long will I be at my externship? For month long externships, it really is nice to have a car at your disposal. Having a transportation is simply convenience, you're not stuck at the hospital/campus or you don't have to depend on others for rides.
For one or two weeks externships, I say, you really can do without a car, anytime period longer than that, a car would be nice.
Second question you must ask yourself, where will I stay during my externship. If you're allowed to stay in the call room for the month, then maybe a car is not needed. But if you're staying at a remote living quarters, then a car maybe needed to get to the externship, to buy groceries, and other means.
So far at all my externships, I've had a car there with me. During my upcoming two externships, one I will have my car (one month long) and the other I will not (3 weeks long). The one externship that I will not have my car at, it is in the major city setting where taxies and subways/trains are much more convenient and readily available.
So questions to ask yourself:
1) how long will I do my externship for?
2) where will I stay during the duration of my participation?
Reasons to have a car with you:
1) to save money (airfare is too much)
2) you need transportation to get to your externship, grocery stores, site seeing (public transportation such as taxies, subways/trains are limited)
3) you wish to bring more of your belonging with you to your externship since you have an apartment rented for the month or 3 weeks, etc.
4) if you know you'll be going on dates during your externship
No clear cut answer, many factors should play on your decision. Good luck in dental school. I'm so ready to graduate already and I still have one whole year left!