I did that drive as part of a group that was heading out there for the weekend. It is something like 120 miles or so, but it is on a two lane road through many small towns for the most part of it. I just looked at Google Maps, they say it's two hours and 30 minutes, but when we did it it took much longer. It's very very very foggy when you get near West Quoddy (at least most of the time) and there are many small parades and town things along the route that slow down traffic.

The street view on Google covers the majority of the route, move that little guy around a bit and you can easily see you won't be doing 50 mph on the route.

Round trip is possible if you head out early in the day. I would not want to drive in the West Quoddy area in the dark, the fog was bad enough in daylight. But you can easily leave say at 8 or 9, get there by noon or 2, spend a few hours there, and even if you leave at 6 or 7 you can be back by midnight.

Hopefully you are going during blueberry season, the route is loaded with them, and many stands of people selling them or stuff made with them.