There are two common first-line anticonvulsants for dogs and they behave completely differently as supply problems.
Phenobarbital is a federally controlled substance, scheduled at the lowest restriction tier but controlled nonetheless. That brings real constraints: refills are limited, early refills are generally not permitted, and a prescription cannot simply be extended over the phone indefinitely. It also requires periodic blood-level monitoring, which means a scheduled visit that itself has to be kept.
Levetiracetam is not a controlled substance. It is widely stocked as an inexpensive human generic, it can be refilled without the same restrictions, and any ordinary pharmacy is likely to have it. The trade-off is that it is usually given three times a day rather than twice, which is its own kind of discipline.
Neither is better in the abstract — that is a decision for your veterinarian based on the dog. What is worth understanding is that if your dog is on phenobarbital, the calendar matters. You cannot fill it a week early because you are travelling. A holiday weekend is a genuine planning problem. Running low on a Friday is not solvable by good intentions.
Where Newark helps is density. Ask your veterinarian for a written prescription rather than taking a clinic-dispensed supply, and fill it at a pharmacy you can walk to. In a city this compact that is realistic, it is usually cheaper, and it means a resupply does not depend on the clinic's opening hours. Keep a written note of the exact drug, dose and timing somewhere other than your own memory, since anyone covering for you needs it.