Learn Russian: Мы каждый год ездим на море.

Ездим is a multidirectional verb for travel by vehicle. We use it here because of каждый год (every year). It describes a repeated, habitual round-trip rather than a single journey happening right now in one direction (which would be едем). We use a driving/riding verb instead of a walking verb (ходим) because people generally travel to the sea by transport!

Why do we say на море instead of в море?

In Russian, when going to the beach or a coastal resort, you use на (onto/at). If you used в to say в море, it would mean literally going into the water to swim or sailing out onto the open ocean.

Is море in the accusative case here? It looks like the dictionary form.

Yes! Whenever you go to a destination, that destination takes the accusative case. Because море is a neuter noun, its accusative form looks exactly the same as its nominative (dictionary) form.

Why doesn't каждый год have a preposition before it?

To say every year, every month, or every day in Russian, you don't need a preposition. You just put the time phrase directly in the accusative case. Since год (year) is an inanimate masculine noun, каждый год doesn't change its ending.