Vizcaya is closed on Tuesdays. That is the single most itinerary-breaking fact on this site, because Tuesday is a common arrival day and because nothing about the place suggests a weekday closure.
If your only full day is a Tuesday, do not attempt a workaround. Put Coconut Grove in the slot instead — it is seven minutes away, it is free, it has the tree canopy Vizcaya's gardens lack, and the bayfront walk there covers similar ground emotionally. Or swap in the downtown museum park, which opens every day.
If you have two or three days, place Vizcaya first on the board and build the rest around it. It is the least flexible item you have. A booked morning slot fixes the day it sits in, and everything else in this city can move.
If you are here on a long weekend, be aware that Saturday and Sunday morning slots go first, particularly in the dry season from December through April. Book those before you book anything else.
One more timing trap: the last admission is well before closing, and the gardens take longer than people expect. A four o'clock arrival is not a visit.