Basic checking accounts can be opened without an appointment at most any local branch. Many of them have $0 fees! You may need $50 – $100 as a first deposit.

Regions Bank
For students 25 or younger. No monthly fee.
LifeGreen® Checking Account For Students

Capital One
Debit card included. Links to parent accounts. No monthly fee.
MONEY teen checking account.

Chase
Savings account included. No monthly fee.
Chase First Banking – Ages 6-17
Chase High School Checking