Ditch the Quinta, bad area from what is said on Tripadvisor.com
If you want near the port, try either Intercontinental downtown (right across the port & you can see the ships come in, its next to the Marketplace) or the Holiday Inn Express, which is like a block or two away.
Both are safe, but its Miami, so don't do any crazy walking late at night. People have been robbed.
South Beach? Pay a penny....you are at the edge of Spring Break. But here's some hotels right on the beach:
Four Points Sheraton
Couryard by Marriott Oceanside
Fontainebleau (undergoing construction on a new building)
Go to their websites for pricing, you might find lower than the usual Internet companies.