I live in Miami and go to Bayside occasionally.
It's safe to park there. There is parking as you enter the area for a fee. I think it's like $5, but not sure.
If you have time, there's a nice boat tour that takes you past the cruise ship pier and then over some of the wealthy islands and you get to see some nice homes from the water. There are alot of stars who live on those islands.
A good place to eat is Bubba Gumps in Bayside and there is also a Hard Rock Cafe and some other restaurants. Lot's of kiosks also.
I assume you are also staying in South Beach. I never heard of North Beach. It might be harder to park there, you might want to contact the Visitors Bureau online and see if you can get some information on parking.
2008 Liberty OTS (Caribbean)
2007 Summit (Alaska)
2006 Century, Infinity (Panama Canal), Summit (Hawaii)
2005 Millenium, Voyager of the Seas, Jewel of the Seas B2B
2004 Explorer of the Seas, Constellation (Canada/New England)
2003 Horizon (Bermuda), Summit
2002 Explorer of the Seas, Brilliance of the Seas (Caribbean)