Central BBQ is tops in Memphis, everyone wants to go to Rendezvous thanks to Hollywood, it's good if you like dry rub, but Central is better.
Peabody's full menu is available at the bar if you don't want to mess with reservations/long waits.
In Little Rock:
Lost 40 Brewing - Decent bar food, good bratwurst, actually decent micro brew beers, Honey Bock is good, Day Drinker is good.
Flyway Brewing - Similar to Lost 40 but in North Little Rock, smaller, decent menu of bar food/heavy hor devours and burgers.
The Root Cafe - Good Americana grub, great breakfast, all locally sourced from AR farms. It is VERY granola and rainbow flag though.
Samantha's Tap Room - Wood fired grill food, Pork Chops are good, quail is awesome, their Asiago cheese grits are my favorite side. Jewel's mom couldn't remember the name Samantha, just Tap Room, when recalling us taking her there, she got frustrated and called it, "some lady's tap room," which has gotten Jewels and I to refer to it as "Some Bitch's Tap Room."
Bruno's Little Italy - next to Samantha's is okay, a lot of folks really like it, It's better than Olive Garden, but I've had better Italian in Arkansas even.
Capeo - North Little Rock, better Italian than Bruno's in my opinion but it's "fine dining" and you'll probably need a reservation on the weekend.
Three Fold - Noodles and Dumplings
Brave New - Probably my favorite restaurant in LR, reservations probably a good idea, nothing on the menu is bad.
Faded Rose - Decent Cajun food, probably some of the best you'll get north of LA - it helps that we share a border with them.
Maddie's Place - Right next to Faded Rose and also decent Cajun grub.
The Fold - Decent, maybe over priced, gourmet tacos.
Aji Ramen Bar - I've not tried all the ramen places, Aji is really good though. If you like spicy ask for the chili paste, they'll bring you a tiny little bit, and it will light your world on fire, use it sparingly.
The Butcher Shop - Steakhouse
Sullivan's Steakhouse - Pricey steaks
Arthur's Steakhouse - Even more pricey steaks
Ocean's - Right next to Arthur's, it's seafood and decent sushi.
Wright's BBQ - A lot of folks claim it's the best in the state, it's good, probably the best brisket, their beans aren't my favorite.
Whole Hog - the OG best BBQ in the state, better pulled pork, beans, and potato salad than Wright's. Wright's probably beats them in ribs and Brisket though.
Eat My Catfish - name is pretty self explaintory
Wasabi - Good sushi and Asian cuisine
Kiyen's Kamikaito - NLR Probably the best sushi in the state, wish he still had his old location, new one is inconvenient for me.
Big Orange - Decent burgers
Potbelly Sandwich Shop - it's a chain out of Chicago but there aren't many in the south, only 2 in AR, both in LR, their "The Wreck" is a dang good sandwich, add bacon and mushrooms.
The Croissanterie - I haven't eaten there yet, but I've heard good things, every thing served on made-in-house croissants, even burgers.