BJ limits are usually higher at Horseshoe on the busy nights. Table games are good however with 5$ Craps and Blackjack easy to find at Ameristar and Harrah's. That being said, the average slot payback is about 90 % which is the worst payback % of all the casinos in Iowa and about 2% lower than the Vegas strip so dont be surprised if you are a slot player and go home broke. Ameristar has the best playing slots ( according to the Iowa State numbers published in the American Casino Guide ). The Horseshoe ( also run by CET - formerly Harrah's ) is the nicest layout and not on a riverboat. IMO - Skip Harrah's altogether its pretty low end. You could check with the Casino or with your hotel
Not sure about shuttles since I live here but they are pretty close to Downtown Omaha - just a bit south across the river.