When should I apply for a visa instead of an ESTA?

If you intend to arrive in the United States aboard a non-signatory air carrier.
If you intend to visit the United States for more than 90 days.
If you believe any grounds of inadmissibility of the Immigration and Nationality Act § 212(a) apply to you, you should apply for a nonimmigrant visa before traveling to the United States.
If you are traveling to the United States for a purpose other than short-term tourism or business.

Completing Your ESTA Application