I'll be staying at the Coral Gables Hyatt for two nights (Friday and Saturday). I've never been to Miami before and don't know where to eat. What are the best few steakhouses in Miami in general, or close to our hotel?

I don't know about steakhouses in that area -- this isn't Chicago, you know. But I can't imagine staying at the Coral Gables Hyatt without splurging on amazing dinners at somewhere like Norman's or Ortanique. These are restaurants that are so special to the area.

Nationally known steakhouses in Coral Gables include Ruth's Chris (you could walk) and the Palm. Flemings just opened (you could walk). Downtown Miami (about 15-20 min away) has Mortons and Capital Grille. Christy's in Coral Gables is a well-regarded local steak house (10-15 blocks from hotel). For Brazilian rodizio (steak and other meats on skewers brought to your table), there is Porquao in downtown Miami.

The original Shula's Steakhouse is in Miami. This is a chain originated by the former coach of the Miami Dolphins. They have a 48-ounce porterhouse. I think the deal is if you finish the steak then you get to quarterback the Dolphins

you must go to Christy's ( a local gem with out of this world Cesar Salad) or Flemings. The Ruth Chris is just ok. And the Palms is quite good. Flemings would probably be walking distance. And Christy's is about 1.5 miles away. My pick owuld be Christy's as it is not a chain but Flemings (if you don't have one in your area) is very good.
Other great restaurants in the area:
Mundo
Normans
Chispa
Versailles
Randazzo's

Although this is in South Beach and not the Gables, I think that the best steak house--and one of the best restaurants in Miami is Prime 112. It is located at 112 Ocean Drive. I suggest calling ahead, however (regardless of what the review says below) I have not had much difficulty getting a table, as long as you are flexible on the time. I do suggest that if you get there early, or if you have to wait for your table which is highly likely--have a drink at the bar and enjoy the delicious hot bacon they place in beautiful wine glasses instead of the traditional peanuts!!! I have not had one thing that wasn't absolutely amazing at Prime.
From Epicurious:

"Hands down the hottest table in town right now, this clubby steakhouse is housed in a Miami Beach hotel that dates back to 1915. Despite the crowd of slick-haired expense-accounters and dressed-up scenesters, waiters in butcher's aprons, dark wood walls, and a Sinatra-heavy soundtrack give the place an old-school feel. The menu is equally traditional, featuring dry-aged prime beef in all its cuts and a vast raw bar. Owner Myles Chefetz claims to turn away 400 customers every Saturday, so be prepared to be waitlisted. If you do get in, try to snag one of the handful of spots on the patio out front to avoid the crowded dining room."