My adult daughter and I have never been to the Boston/Martha's Vineyard area and I am seeking advice on how to spend a 3 day vacation there. We get there on a Saturday morning and leave on Tuesday early AM (October 12-15). We would like to do as much exploring as we can and take the ferry to Martha's Vineyard or Nantucket, but don't want to cram too much in and miss seeing all Boston has to offer. Thank you so much in advance. So far all we have are airline tickets and not much time to plan.

Travel time from Boston to MV is around 3 to 3.5 hrs each way. If you left Boston at 7am you could catch the 9:30 ferry from woods hole that gets you onto MV at 10:15.
The 5pm ferry would get you back into Boston by 9:30 or 10. That would give you 6-7 hrs on the Island to explore. So as long as you don't mind the 6-7hrs travel time round trip you could easily that into a day trip.

If you don't have a rental car you'd need to factor in wait time to catch a bus.

It's not a day trip I'd want to do, but nothing wrong with it, per se.

You only have two full days so I suggest that you skip the Cape and the islands this time. It's not enough time to visit MV or Nantucket and leave enough time for Boston. Either of them can be a pretty full on day trip from the Cape itself by ferry, never mind from Boston. If you stay overnight there you won't have time to see much of anything in Boston. You also would need a car. I would leave more like 3 to 3.5 hours from sail time. Traffic south of Boston can be killer at any time, getting out of Boston depending on where you're parked can take time, and you need to park in Woods Hole and get to the boat or get in queue for the car loading process if you're taking it (I would suggest not).

Keep in mind that the ferry alternates between Oak Bluffs and Vineyard haven this time of year. They aren't that far apart but it's a consideration (the example times given by J62 are arriving and leaving from different towns on MV).

I don't know how practical it is but you could look into flying to MV or N from Boston and skipping Boston altogether.

If it were me, I would stay in Boston the whole time and instead of MV or N, you can easily visit the Boston Harbor Islands as a reasonable full day out on the sea (2 islands visit) or half day (single island visit). No car needed, leave right from downtown Boston. Even that eats into your precious little time in Boston but I think MV or N would be far too much for the day to be any fun. I believe the island ferry ends on 14 Oct and free on the 13th.

It is all on the weather if the ferry is even running. Check first before taking the trip. A boat trip to Salem is fun from Boston Harbor but there is really enough to do and see in Boston. Enjoy the fall colors and great food.

Make a list of what you want to do in Boston and see if you can spare the time for MV. I'm with the others. I don't think there's enough time and weather is iffy in mid-October. Last fall we enjoyed watching some festivities in Chinatown and then walking the Rose Kennedy Greenway to Quincy Market. Boston North End food tour is fun but since we had done it before we did a South End tour last year - a part of Boston we really weren't familiar with. My favorite exhibit at the JFK library was Jackie's clothing but I don't remember if it was a temporary exhibit or not. We usually get tickets for an evening show some place. I love dim sum lunches.

We'll be visiting at the same time. For something different there happens to be a chocolate festival going on that weekend in Boston.
https://nechocolate.org/

I forget what it's called but the oldest bar in America is in Boston! Look it up

I would stick to Boston only. Because you are so short on time. Also the time of year. You can't even begin to scratch the surface of a city like Boston in only those few days. If you try to fit in the others, basically you wouldn't have any time left for the city things.

https://www.bostonharborcruises.com/...dule-and-rates

You can whale watch from Boston harbor, if you like getting on the water. Or go to Provincetown for the day.