you can look up kasasa to find banks near you with higher interest checking up to 10k-25k. the problem is that the both require direct deposit and debit card transactions. in my case the best/nearest one requires 12 signature debit transactions which makes it useless for me. i wont use a debit card that often. others without signature required, you can do things like buy X number of $1 amazon gc's with the debit card to add to your account.
another option for those that like to maximize exposure and have enough taxable accounts to withstand a 40-50% hit to the funds and still have enough to make your emergency needs is to invest your emergency funds into whatever combination of total stock market/total international market or whatever fund you like best and switch the same amount of cash in your retirement vehicles to bonds/stable value/tip funds (whatever floats your risk boat).
if you hit an emergency, you sell whatever you need out of the taxable accounts and move the same amount out of the retirement fixed income to equity. net effect is your asset allocation remains the same and you get to avoid taxes as your income generators are sheltered. if your taxable funds are up, great you made some money but have to pay more taxes, ideally the funds having been established long enough to get long term capital rates. if the market tanked, that sucks but, you get to now tax loss harvest those equities in the taxable side and get income deductions to offset potential future gains.
again, this only works if you have enough funds to withstand a potential 40-50% haircut in equities.
do i do this? not with my emergency funds. wife is less risk inclined as i am, so we do the traditional bit and have a nice worthless money market account to hold our 12 month emergency fund.