Your Miami expert is here. Lived there at some point, spent my summer growing up and have had family there for 30 years so I go quite often. We just spent 10 days there in January with our family group. There are different spots in Miami that can seriously alter your perspective.
Some loose thoughts:
-I rarely ever go to Miami Beach. It's a weird combination of people looking to party (bachelor/bahelorette parties, europeans, people fleeing the cold, and some latinos). That translates into quite a few tourist traps and overpriced spots. Having said all that, Miami Beach is one of the few walkable areas of Miami, and during the day it can be fun to check out Lincoln Road. Also, the beach is actually pretty good, particularly if you stay at a hotel with beachside access (the Loews is very well located). Joe's Stone Crab is great and worth the visit...go off hours to avoid the wait (the fried chicken is cheap and a great way to balance the table).
-others have made some good recommendations. My kids always loved the zoo, but they were a little younger. Its a pretty long drive from Miami Beach. Also be warned if its a sunny day you might get roasted so plan accordingly. My kids loved the Everglades visit. we did one of those Airboat rides that they still remember. Afterwards they will have some alligator show. Still a drive, but not as far as the Zoo. Jungle Island is located near Miami Bech but I always thought it was expensive for what it was. I seem to remember my kids enjoying the Science museum (think they were a bit younger than 13 at the time tbh).
-Key Biscayne is one of my favorite places on earth. Its a village sitting on an island off the coast of Miami connected by three bridges. There are two good parks on the main island (Crandon Park and Bill Baggs) that can be a nice day at the beach. Also has a nice public golf course.
-Coconut Grove is more my speed these days. Plenty of restaurants and cafes. Another walkable area. Has a couple of parks on the water with a view of the bay. They have a fun Farmer's Market on Saturday's.
-Brickell: is one of those boom or bust areas just south of downtown that is currently booming. Plenty of restaurants in this area as well as the Brickell Center, a high end shopping mall. I only mention the mall because it has a great Escape Room operation. I've done it twice with my teen nieces and they had a lot of fun.
-Downtown itself is kind of blah, though the area near the Casey Center (home your Miami Heat) is getting a massive facelift. Just to the north of this area is Wynnwood which is a trendy neighborhood at the moment (as well as the Miami Design District). That Wynnwood area has plenty of restaurants (more on that below) and little stores that could. The neighbourhood is littered with murals of all sorts (it use to be the up and coming artist area).
-for my family, Miami is the number 1 shopping destination with a variety of good malls: Dadeland (large meat and potatoes mall), Merrick Park (upscale), Dolphin (large outlet mall), Aventura (standard mall, slightly upscale just north) and Sawgrass Mills (large outlet mall way north).
Food: the restaurant scene in Miami is hot currently so there are plenty of restaurants available. The two big Miami ties that you should try are the Cuban coffee and the Cuban sandwich (medianoche). From there it really varies on your interests, Miami has some of the best diversity of Latin food with Peruvian, Argentinian, Nicaraguan and some Colombian the most prevalent. Plenty of asian, Italian and seafood places. These are some places I would recommend:
-Joe's Stone Crab (Miami Beach, can be pricey, can be a long wait, see above advice)
-Osteria da Fortunata (Miami Beach) overpriced, but the pasta is damn good. near Lincoln Road.
-Yardbird (Miami Beach) quasi southern food, believe this was the original, they now have some in other cities
-CVI.CHE 105 (Miami Beach, Coral Gables) nice Peruvian spot
-Miami Slice (some of the best pizza in Miami, location is blah)
-Chug's Diner (Coconut Grove) diner food with a creative twist.
-Narbona (Coconut Grove and Key Biscayne) Uruguayan spot with pizza, pasta, and steak
-Mister o1 Pizza (several locations) creative, good tasting pizza
-Wynnwood Burgers: couple of decent spots include La Birra Bar, Cowy Burger and Skinny Louis. they're near to one another, I'd pick the one that has the least amount of wait
Best Cuban spots: La carreta and Versailles are the two staples (not sure I would make the trek all the way there). I seem to remember a good place on MB (Havana Vieja), but there should be other options as well.