Allan if the Alexander is a better fit for your budget then I recommend you book now before they fill up. It looks like a great hotel, the only problem I see is its about 5 or 6 miles north of South Beach, so you will have to have a rental car or figure on alot of taxi shuttling back and forth.
Are you sure you couldnt find anything in South Beach? Did you try the alternate hotels I posted above? They are all walking distance.