Like pp said, there are very few neighborhoods with pools. Several people we know joined the very nice Lifetime facility - they have large indoor & outdoor pools. It was built about 5 years ago. The YMCAs are nice here too though the pools are fairly small. The Zorinsky pool/water park is a big outdoor pool and a family pass is $175.
The airport here is great. So easy to get in & out. There are fewer good airfare deals though.
One thing that is different - while there are buses in elementary if you're over 1 mile away, you have to pay for service in middle and HS, at least in Millard. We live 2 miles from the MS & HS and have to pay if they ride. I think you might be home so that might not matter but know you'll need a carpool or plan to pick up at school.
Some districts have an IB program if that is an interest and many offer several AP classes. Millard has an elementary & MS that also offers IB at that level.
Be prepared for comments if you move. I got questions about if we were going to live on a farm!

People had no idea that Omaha is a nice city and has suburbs with all the modern shopping & conveniences. I was homesick and wanted to move back to VA for about 5 years but it really is a nice area and great for kids. Good luck!