For hotels, check out the Doral area, near Trump Doral. Decent hotels there for that price range and you'll be close to major highways. Very safe too. Check out Aloft Doral.
I'd stay away from Miami Beach. You'll get ripped off. Everything is overpriced especially hotels and dining. Just good for taking a stroll through ocean drive.
Doral also has a new shopping center called Cityplace. Good restaurants, live music, movie theater and bowling.
http://www.cityplacedoral.com/
Dolphin mall is a great choice for tourists. Also good food and entertainment. Kids will like Dave and Busters and the bowling place.
For adult fun I'd check out Seminole Hard Rock Hotel and Casino.
Wynwood might be boring depending on the age of your kids. The most interesting attraction there are the art murals that cover the walls throughout the eight square blocks or so. A few art galleries and overpriced dining. I usually just drive by or take a brief stroll when I'm showing family or friends that visit.
Lastly i would also recommend taking a drive through Sunset Place and Coconut Grove, lots of family-friendly dining spots. Sunset place also has an arcade place the kids love.
For adult fun, Sunset Place is also within walking distance of BT's Gentlemens Club which I find to be the best strip club in Miami. Not as big as tootsies but great experience overall.
One last thing. Stay away from the Miami Science Museum. Huge rip off, a lot of nothing and a big waste of time.