I opened Washington Mutual (WaMu) checking and savings accounts at the same time in December 2006. WaMu was offering to pay 5% interest on your savings account if you opened both accounts thru the promotional link on the website. I always see this promotion being offered so it may be offered even now. This 5% interest was competitive against other banks at the time. I wasn't too happy with the customer service the few times I went in to the branch/called customer service. I even had to wait 10 business days for a check to clear once. The customer service representative said that the long waiting period was because I was a new customer and once the average daily balance establishes a history, the checks will clear much faster. oh well. It was so frustrating, so I kept my Bank of America checking account. I just transfer money to my WaMu savings account (thru WaMu, BofA charges a fee if you do it thru them) from my BofA account. I only use WaMu for my savings account. I thought the rate would fluctuate but I'm still earning 5% even now.
It takes a while (4-5 business days) for the money to transfer. I put in a transfer from my B of A account to my WaMu account on Monday morning and I didn't see it hit my WaMu account until Friday morning.
Also, you can withdraw the money anytime from an atm machine. WaMu sends you atm cards for both accounts. If you forget to bring one card, you can transfer money from checking to savings (vice versa) at the atm and then withdraw money. I used to have a Capital One savings account. Capital One's interest rate was comparable to WaMu's. However, Capital One did not give you an atm card. To withdraw money, you had to transfer money from your capital one savings account to your bank/brokerage account which takes 3-5 business days.
I like Bank of America because the atm machines are everywhere here in Los Angeles. In Beverly Center. BofA's are also easy to find in San Francisco and Las Vegas (Caesar's Palace shopping area).