It's true that there is no cheap way to access Admirals Clubs on a domestic Coach ticket unless you have at least oneworld Sapphire status from another oneworld airline. However, if you wanted to try AA before the Amex Centurion Clubs open, you might consider getting a credit card that gives you access to Priority Pass restaurants, and not just Priority Pass lounges.

The US Bank Altitude Reserve card provides four annual Priority Pass visits (including restaurants) to cardholders. After annual travel credits, the card's annual net cost is just $75, which also gets you twelve GoGo WiFi passes, and primary car rental LDW. All "travel" charges (as defined by US Bank) and all mobile-wallet purchases also earn 4.5% back, applicable to future travel (subject to certain minimums on lodging and rental-car charges).

The Chase Sapphire Reserve will have a somewhat higher annual net cost, but includes unlimited Priority Pass lounge and restaurant visits, as well as primary LDW.

Currently, Bobby Van's Steakhouse -- in the AA terminal at JFK -- is a participating Priority Pass restaurant.

There are no Priority Pass lounges or restaurants in the LAX AA terminal, but there are some in the TBIT and LAX T7, both of which should be accessible airside from the AA terminal.

Edited to add: If you're primarily a Hyatt guy, and can achieve WOH Globalist status, you might be interested in this recent FT thread:

Offered AA Executive Platinum (targeted for 2019 Globalists)

While it's true that even AA EXPs don't get lounge access on domestic Coach flights, EXPs should be treated very well by AA -- and you would get free MCE seats, free checked bags, etc.,etc.