Car rental location near Fuji. Shin Fuji vs Mishima Station

Looking for input on my car rental plans for Fuji. We'll be taking the Shinkansen from Nagoya to Shin Fuji station or Mishima station. We are lodging near Lake Yamanaka. I was originally looking at booking a Toyota Rent A Car near Shin Fuji station. I am now seeing/considering booking at the one near Mishima station instead since we'll be heading to Tokyo after on the Shinkansen. We are only renting a car for the Fuji portion of our trip. Is there any reason not to book at Mishima if we're going to take the Shinkansen to Tokyo afterwards?

by pftossitaway