The Breakfast Club in Moscow is good if you can get in.
Alehaus Moscow has killer burgers. - if you can get in.
Patty's Kitchen or Casa Lopez in Moscow are both decent Mexican food - if you can get in.
Bucer's Moscow has Guiness cake to die for - if you can get in.
The Pie Safe in Deary has been mentioned. They have a full menu, but this is where you buy fancy cheeses to take home for gifts.
Potlatch has a food truck called the Savory Bee. Good burgers but the worst fries on earth, IMHO.
Also a bar called Codi Jo's Wagon Wheel which serves breakfast and lunch. It's not bad
Big Timber Cafe in Harvard. I've never been but my granddaughter likes it. They are open when they are open. They post their schedule a couple of days in advance on Facebook.
Gas station pizza in most small towns. Drive up coffee virtually everywhere. Almost every town has a bar that will make a burger.
Most of these places will take you stinky in camo. If you go to Pullman they may want you to shower.
As far as food along the way, are you on I-90 all the way or coming over Hwy 2? Hwy 26? I advise you stay on I-90 as long as you can. Cut over at Sprague, WA. Be careful on Hwy 23, some of those corners will ruin you if you hit them too fast. Hwy 26 is the preferred route for WSU kids traveling home and back. It backs up and folks get aggressive and stupid.
Idle Hour Quincy - Don't waste your time anywhere else in Quincy.
Michael's on the Lake Moses Lake - Fancy and very good.
Caverna Royal City - bring cash
South Fork Cafe Pullman - if you can get in.
Birch and Barley Pullman - the best rare steak if you can get in.
The Palouse Caboose , Palouse, WA - Great sandwiches.
If you are coming in on Hwy 26, nothing from Othello to Colfax. Plan accordingly. There is Chester chicken at the gas station at 26 & 395. Surprisingly good but truck stop expensive.
You may have noticed a lot of "If you can get in". University students pack all the best places in Moscow and Pullman.