Get your comfy walking shoes on and plan to spend at least one full day. Two days are really needed to properly enjoy the whole experience. If it's hot and you're tired, take a break at the IMAX theater.
Some zoo exhibits make you want to cry in sympathy for the animals. You don't get that here. Lots of space and well kept.
Sometimes a zoo may be part of a more national scale membership group, so if you are a member of your local zoo, there may be a reciprocol agreement that gets you reduced entry fees in Omaha.
Foods are not the best, and overpriced of course, so pack a picnic lunch and some drinks.
Make sure you do the train or the tram to take a walking break and see the exhibits from different angles. The acquarium is a favorite as is the dessert dome. Love the tigers and bears and monkeys. Other places have better bird areas, but this zoo is always changing and growing, so who knows what the next expansion project will bring!