You'll need to forget about any of the American Express properties unless you significantly increase your budget. That said, there are many properties that you can get into for $200/night (including some name brand hotels -- Hampton Inn, Residence Inn), although none that I have any experience with. You might be best off doing a search on a site like hotels.com and relying on tripadvisor and other online reviews. Certainly booking now will help, as is the fact that you will be there mid-week. But don't wait too, too long to book, as that is prime time for Miami Beach.