We are traveling to Boston in October. Our rooms are booked for four nights there. We are thinking of renting a car and driving to Maine for the day returning late that night. Any suggestions? Should we drive or use the train?

Depends on what you want to do...If you want to go to Portland and walk around, you could take the train, but it would be a very long day trip. If you want to see a little coastal scenery you should probably rent a car for the day.

Where in Maine, and what's your goal?

Why is this tagged Oklahoma?

I vote for renting a car. You can stop along the way. If it's early to mid-October, you could take a foliage cruise out of Portsmouth NH.
In Portland, probably park in the garage next to the ferry to enjoy the Old Port Area. Fun little shops.

If you want to do some beach walks, southern Maine beaches are great.

Great we will probably rent a car. We just want to see foliage and hopefully some lighthouses. I just know nothing about the area!

What is your goal for going to Maine (and where in Maine)? Do you want to see the coast? Do you want to visit another city/town? Do you want to see more foliage?

Unless there's a very compelling reason, I'd vote for renting a car and driving to places that are closer. There are plenty of places in MA and NH that are just as nice and the drive is shorter...

If you're looking for fall foliage, I would not recommend Maine, or at least that part of Maine that's realistically within a day's round-trip from Boston. Places in New Hampshire and central and northern Mass will provide far more colorful trees and topography that's suited to foliage viewing. If you search in this forum for foliage/Massachusetts/NH, you'll find lots of suggestions for different routes to take.