The closest boat ramp to Star Island is on Watson Island, by Parrot Jungle. The ramp is owned by the City Of Miami and the fee is $10. Parking is limited, so plan to get there early or else the cops will tell you to go away because there is no more parking. It fills up fast, and is often full to capacity. Not so much on weekdays, but it gets crazy on the weekends. I like the Watson Island ramp as it is reasonably well maintained (the County ramps are in better shape, but the Watson ramp is not terrible), and the cops are there all the time so it is "safe". Or at least as safe as can be expected in this place.
Avoid the ramp on Purdy Ave on Miami Beach. It is closer to Star Island than Watson Island, but there is really no parking at all. The ramp is mainly there for the police boats (a number of which live at that ramp) and people who launch kayaks and stuff.
You can go to
http://www.miamidade.gov/parks/fun-marinas.asp for a list of all County marinas. Miami-Dade County Parks dept has excellent ramps. Fees went up to $15 on the weekends and holidays, and I think it is $12 on weekdays. Fees went up when budgets dried up.
Also note that Crandon Park Marina on Key Biscayne has a $9.50 toll if you have a single axle trailer.
I do not launch in Broward County very often. I am really only up there once a year, for the Winterfest Boat Parade. I volunteer as a control boat which allows me to anchor away from the public in the "restricted" zones. Anyhow the only Broward ramp I have used is the 15th street ramp close to Port Everglades. To be honest - I think it sucks. I have not seen ANY public Broward ramps that impress me. The 15th street ramp has limited parking and only TWO ramps. Compare this to Watson Island (one of the "not so good" Dade County ramps) has 6 or 7 ramp slips. But to launch a ski I suppose the Borward ramps are decent enough. Again - parking at all the Broward ramps I have seen is limited - but most people up there do not trailer. They have a dry stack or something. I do not know how packed the ramps up there get.
Pompano is a decent haul from Miami. I would say it is a good 50 mile haul one way. In the city with normal traffic - it is easily an hour. Maybe more - depending on the traffic pattern in place.