I'm ~1 hour back down the coast in Machias. I've not been sightseeing much up towards Calais so don't really know what if anything is up that way. It may be a bit chilly, but sightseeing spots between Machias and Calais include Jasper Beach in Machiasport, Roque Bluffs State Park and beach in Roque Bluffs, Reversing Falls in Pembroke, and Quoddy Head Lighthouse in West Quoddy. For hiking there's the Cutler Preserve, although I don't know if the snow will be gone or how muddy it might be.
Don't know much about indoor things to do. Eastport appears to have more artsy stuff, but don't know how much is open. If you do go to Eastport drive the speed limit from Rt 1 into Eastport. That section of Rt 190 goes through a tribal reservation and traffic fines are a big revenue source.
For places to stay to make it a weekend I'd recommend
West Branch Farms in Machias. They have cottages and a decent restaurant; do note that the restaurant is down the road a bit from the cottages (i.e. not walking distance). It'll be ~1 hour to Calais, but closer to stuff in Ellsworth (~1.5 hours), Mount Desert Island (~2 hours), and even Bangor (~2 hours) (ex.
Maine Military Supply). Let me know if you end up down this way; maybe we can sync up (or not), your choices.