I would say that taking the MetroMover is safe. I use it all the time to go to Miami Heat games at the American Airlines Arena. It is about a 5 minute walk from the hotel to the station. A cab from the hotel to Bayside would not be expensive, so that might be a good option too. I would probably take a cab back if you head back late.

I have never been to the children's museum but I have heard very good things about it. It is not far from the hotel. There is also Parrot Jungle (believe it is now called Jungle Island) in the area which might appeal to kids.

Hope this helps a bit. Let me know if there are any other questions or you need any recommendations.