Yarinacocha is the best place around to get good food. It is a couple of miles outside of Pucallpa, but worth the trip. Go to the restaurant Anakonda.
A hidden gem, a block off the plaza in Yarinacocha is "Parilladas Orlandos". They sell a wide selection of barbecued meats, and the quality and price is excellent.
If you're not up for the trip to Yarinacocha, you still have plenty of great options. On the Plaza de Armas in Pucallpa, is a gem of a restaurant called Portal Chicken. Their specialty is Pollo a la Braza, a Peruvian favorite. For $3 USD you can get a quarter chicken with french fries, and the food is excellent. Their frozen lemonade is also quite tasty. For the cost of round trip motocarro fare from the plaza to your location, they will deliver to you.
About 2 km from the airport, on Calle Alamedas, is a seafood place called Mijanos. It like all other seafood places in Pucallpa is only open for lunch noon to 5 pm. It serves imaginative dishes with seafood that is as fresh as can be gotten in Pucallpa. Their chef had culinary training in Lima, and it shows. The biggest downside about Mijanos is that it is quite pricey by Pucallpa standards nearly $30 USD for two people, including a shared appetizer and 2 beverages.