... that we suggest exploring one at a time. The suggestions below are presented in ascending order of distance from Coral Gables (closest to farthest). Given how competitive the Miami restaurant scene is, a good indicator of quality is how long a place has been in operation!
All of the wedding celebrations will be held in Coral Gables, one of the oldest neighborhoods in Miami along with neighboring Coconut Grove. Coral Gables is essentially a suburb of Miami that was developed in the 1920s under the City Beautiful philosophy of architectural reform (a precursor to what we call master planned communities today). Unlike the rest of Miami, you won't find tall, modern apartment buildings here. The Mediterranean Revival style prevalent in the neighborhood was mandated in its original plan and continues on today.
Here's how we would walk through the Gables:
Coconut Grove ("the Grove") is like the big sister to Coral Gables. It's equally charming and historic but offers gorgeous views of Biscayne Bay. In recent years, the center of the Grove (CocoWalk) has morphed into a yuppie millennial playground, and gateway city institutions like Salt & Straw (ice cream) and Sadelle's (a luxury deli experience) have joined in on the fun. Fear not... plenty of more authentic culinary experiences persist, including:
Drinks:
Little Havana is one of our favorite places in Miami. The vibrant colors, the wild chickens running around, the homemade food and drinks... what's not to love? The center of the neighborhood is 8th Street ("Calle Ocho"... yes, like the Pitbull song) and we recommend staying near there if you're on foot.

Brickell and Downtown Miami are the urban core of the city and offer beautiful views of Biscayne Bay, the cruise terminal, and Miami Beach and the Atlantic in the distance.
Once home to Miami's artistic community, Wynwood has become another yuppie outpost. But it's still a ton of fun and a great place to hang out at any time of day. The Design District is the closest thing Miami has to high-street shopping, and there are some excellent food options there as well.

Wynwood:

Design District (including Midtown):
If you're escaping winter weather, we'd definitely recommend spending some time on the beach. We wouldn't be surprised if some of Kate's Canadian family even jumped in the ocean! There are several neighborhoods on the beach, but here are a few of our favorites:

South of 5th (southernmost part of the beach)

South and Mid Beach