Here are your options if your main concern is to avoid ATM fees:
1) Which bank's ATM network is closest to you whenever you need cash? Is it BOFA, Wells Fargo, Washington Mutual, CitiBank, etc.? Get a checking account with that bank, most banks offer an "ATM only - FREE" checking account which has no minimum balance requirement and no monthly fees.
2) Join a local Credit Union. My credit union charges $0 transaction fee if you use another credit union's ATM and they have ATM's everywhere.
3) This is the best option, you can keep your current debit/check card and pay $0 for withdrawing cash. How? Use a POS terminal for debit cards at your local Safeway, Von's, K-Mart, Walmart, Target, Albertson's, Fred Meyer's, even the USPS. Basically anywhere that has a POS terminal, you buy groceries or something small (that you need) slide your debit card, press debit card, enter in your PIN and the amount of cash you want back.