If nuhusker is available, he's the go to guy for Omaha. I'll post to keep it "up on the board". When I was researching for a possible College World Series trip, the Omaha Marriott had two concierge levels per their Fact Sheet and had what looked like from the photos one of those indoor/outdoor pools (it wasn't close enough to the downtown ballpark for me).
Also, there's some good info over to the right in the More Like This column
If you're looking to be close to the TD Ameritrade park, your options are probably CY in Old Market or FFI just a couple of blocks from ballpark. The pools are every Omaha location are typical Marriott pools. The Marriott looks old and outdated from its exterior design but was remodeled just a few short years ago. Rooms are typical Marriott layout. The concierge lounge is staffed by professional, friendly staff. There's a CY around the mid-town area where AKSARBEN used to be. I prefer the CY farther west in Lavista. It's quiet and once you learn your way around it's relatively convenient to get to/from. Enjoy your trip.