I've been to this museum several times, each time out of town visitors come they want to go and I really don't mind seeing it again. They have a great movie to start you off with the history of the Arabia. Then you get to walk into the museum and see all the artifacts they brought up and restored. It's and amaizing slice of the past that was saved by of all things mud! The last time I went I took my 20 month old and she wasn't so impressed, she liked running around yelling "Arabia" but they don't have anything to keep little ones busy while everyone else looks (that's why I didn't give it a full 5 star rating).
Make a day of this! Its located inside the River Market, so go check out the vendors there and then venture inside to check out the huge functioning water wheel that was once attached to the steam boat. Once inside the exhibit you will be taken for a tour and learn a lot of interesting facts and see all of the things that were saved from the bottom of the Missouri River. This is a great place to take older children!
This is a museum of an old ship that was found in a farmers field. The museum is interesting, with videos and a giant water wheel from the ship in operation. It may be a little slow for small kids but they are sure to love the gift shop and snack bar. Could be priced a little lower for what it is but still interesting.