Work it through concretely. A puppy year involves a vaccination series, a spay or neuter, and a handful of follow-ups. A dog with recurring ear trouble adds a recheck two weeks after every course. A dog on anticonvulsants adds periodic bloodwork. A referral to a board-certified specialist means travelling to whichever borough that specialist practises in, at whatever hour the appointment falls.
None of those can be done by subway with a fifty-pound dog. Ride-hailing services allow drivers to decline animals and frequently do, particularly in the rain, which is precisely when you have an appointment. Yellow taxis are at the driver's discretion. The reliable options — a pet-specific car service, or knowing a driver who is happy to take dogs — cost more and need booking rather than hailing.
The planning that saves the most money is therefore about geography. Choose a primary veterinary practice you can genuinely walk to, even if a slightly cheaper one sits two neighbourhoods away, because the fare difference will erase the saving within a year. Ask that practice which specialists they refer to and where those specialists are, so a referral does not become a cross-borough expedition by default. And identify one twenty-four-hour emergency hospital you could reach at three in the morning, along with how you would actually get there — this is not a decision to be making while holding a dog with a painful eye.
The alternative worth knowing about is the least glamorous one: for a dog this size, in reasonable weather, many of these trips are simply a walk. A breed rated 4 out of 5 on exercise need will not object to two miles across town.