The west suburbs are safer and much more quiet (areas like Davie, Plantation, Coral Springs, etc.)
If you want more of a nightlife and younger crowd, you'll pay a premium for nice safe areas. Lots of things to do in pompano beach or Miami beach, maybe sunny isles. Again, these aren't as family friendly.
Ft Laud is cool, but can be a bit hectic and a lot of traffic. Don't bother with downtown Miami. It's overrated and sucks. The Keys are awesome though and a close drive for a weekend getaway.
Hope that helps.
Edit: As far as areas to avoid... Anything near the airport, downtown around 95, parts of Hollywood are dicey. Just my opinion though.