Go for bank incentives
Opening a new account? Check out bank incentives, such as cash bonuses.
But you'll have to meet requirements, such as maintaining a minimum balance to avoid a monthly fee, using direct deposit and keeping the account open for a certain length of time.
Less commonly, you'll find banks that offer referral bonuses. But be careful about making a long-term commitment with a bank that offers a bonus. You may find that standard interest rates are puny.