Where do you currently have your EF? And what is your hesitation with a high-yield savings? Do you not know/trust the bank?
I've used high-yield savings accounts since I was in college. Here are some things to look for:
-FDIC Insured
-Look for fees. You should not be paying a monthly fee. There may be fees on excessive withdrawals, standard is 6 free withdrawals per month. This is standard as it was tied to a federal regulation (that is now gone), but many banks still have this fee and as this is your EF, it really should never come into play.
-Look for any fine text that lists the rate as being introductory. All interest rates are subject to change at any time, but don't get fooled by a bank that says they'll give you 4% for your first three months. It's best if their rate is the standard rate for all customers because it means it's less likely to be quickly reduced after they lure in new customers.
-Probably worth a quick google search to make sure they aren't in the news for anything stupid. Also good to check to see how their customer service is, in the rare occasion that you actually need to use it.
If you are hesitant of why these banks are offering higher interest rates then your local bank, two of the main reasons are that they are trying to attract more money to their bank so that they can in turn lend out more money (for their profit and partially yours), and that they are (most likely) an online bank and don't have all the costs of a standard branch network.