The Beachmere has a pub that opens at 4pm and has ocean views. I've never been there but been curious ...
A great place in Perkins Cove for drinks would be the MC restaurant and bar, there bar is on the upper level overlooking the ocean, the places also has great food. If you want to be on the main beach for drinks try Splash, its part of the Norseman Hotel thats directly on the beach.
Picture of the place I took
Keep in mind that there are a few restaurants at both Perkins Cove and on the main beach of Ogunquit that have restaurants with views.
The Oarweed is right at the end of the Marginal Way in Perkin's Cove and is next to the water.
In addition to what's already been suggested, Barnacle Billy's has a nice balcony out back that's perfect for a quiet drink in the sun with a view of the harbour. It's a nice place to sit for an hour or 2 watching the ducks and the bass as well as the boats coming through the drawbridge.
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