Some credit unions and local banks offer high yield checking accounts that pay an above market interest rate in exchange for one ACH/direct deposit transaction and a minimum number of debit transactions. For example, I use Provident Credit Union here in the SF Bay Area. I have one check direct deposited there plus I transfer money over from the regular bank. As long as I make 10 debit transactions a month, they pay me 2.26 percent APY. These accounts have a maximum limit on the amount they will pay interest on at the high rate. Provident will pay this rate on balances up to $25,000. They also refund ATM fees from banks.
My method is to maintain the maximum amount at the high interest rate as savings and spend from the monthly deposit. Between the grocery store, the gas station, and all the other places I go, I can meet the 10 debit transaction minimum.
Check depositaccounts.com for your location to see if someone there offers a similar account. They show Provident as not having easy requirements to join, but that is not accurate. As long as you live in the service area and can use another member as a reference, you qualify. Play with the account filters at depositaccounts.com to broaden the possible institutions on your area.
As far as savings and money market accounts go, the best APY I can find right now is TIAA-CREF via TIAA Direct. They are paying 1.25 percent APY, but that's a promotional rate and could change at any time.
Short term CD's can't match these rates.