Summer is the season when New York is crowded with tourists from all over the world.

[Mori]

That can be used for people or things in defining relative clauses. However, it cannot be used as a replacement for where or when with the meaning “in which,” “at which,” or “during which.”
Summer is the season when New York is crowded with tourists from all over the world.
Jack C. Richards & Chuck Sandy, Passages 1, p. 110

After common nouns referring to time, when is often replaced by that or dropped in an informal style.
I'll never forget the day (that) we met.
That was the year (that) I first went abroad.
Michael Swan, Practical English Usage, entry 237.7

Isn't season a common noun referring to time? Can't we replace it by that or drop it?

 

[Skrej]

Yes. In fact it's better with neither 'when' nor 'that', in my opinion.

 

[emsr2d2]

Yes. In fact it's better with neither 'when' nor 'that', in my opinion.

I think it's better without "the season" but keeping "when".

Summer is when New York's crowded with international tourists.

 

[Tarheel]

Well, it's always good to remind people that summer is a season. You know -- in case they have forgotten.