The sentence that has no spelling error is:

☀ Children welcome summer vacation with zeal.

Explanation of the options:

☀ Playing and eating are the two prime works during vecation. (Incorrect spelling: vecation. Correct spelling: vacation.)

☀ Ooty is my dream vacashun spot. (Incorrect spelling: vacashun. Correct spelling: vacation.)

☀ Geeta is going to Pune for vakation. (Incorrect spelling: vakation. Correct spelling: vacation.)

☀ Children welcome summer vacation with zeal. (This sentence is spelled correctly with no errors.)