Basically, there are two options. Either you go direct from the Caribbean to the Providence Channel, stopping at Nassau and continuing over the banks to Miami of via the NW Providence Channel to Florida. The other option (which I took) is to go by short hops from St Martin to St Croix, then the South coast of Puerto Rico, the Mona passage to Samana, Luperon, Providenciales, Mayguana and through the Bahamas bank to Nassau. It all depends on how much time you have...
We took almost exactly the same route as John three years ago. On a typical Atlantic circuit you will be doing this around March and the trades can be a bit strong in the nothern Caribbean, so going south of Puerto Rico makes life easier.
Like John we went from Mayguana inside the Bahamas, and then across the Bahamas Bank from Exuma Sound to Tongue of the Ocean. A decent pilot is needed to find the best passages across given your draught, but it is easier than going outside to the east of the Bahamas.
Incidentally, if crossing direct to Florida from Europe by the trade-wind route, it is still necessary to dip well into the tropics at the latitude of the northern Caribbean islands in order to get the best of the trades. The timing is slightly awkward for a direct passage as December is the best time for the crossing, but its best to get south of Europe before the winter. Many people stop over in the Canaries.
Am currently cruising Chesapeake in Sadler 34 having followed route outlined above. Very much enjoyed Exumas which were highlight of voyage to date. Beautiful islands and coves, what we had hoped to find in Caribbean and did not (we still enjoyed). Drawback all provisions expensive. Arrive well stocked from Puerto Rico & Dominican Republic.
If going to USA you MUST get VISA in advance, easy in UK, difficult if not impossible in Caribbean except for Trinidad.
Intracoastal waterway fantastic if mast less than 55ft and draft reasonable. Many anchorages North of Florida. Marinas in USA incredib ly expensive but usually good. Food storing can be a problem as groceries rarely close to anchorage
East coast as now can be very hot, presently 99 deg F!
Delighted to provide expanded info if needed.