I'm startiing to feel that it's hard to find an outdoor restaurant that DOESN'T allow dogs!!!!! Most will, call to check first.
The swimming places (when you say that, I am thinking beaches) is going to be harder. Many, many beaches are closed to dogs at this time of year, both due to high usage by humans and also nesting birds.
There are however plenty of walking trails and dog parks. There is a website called BringFido.com, which has a good listing of places.
My dog says, "Woof", by which she means, "Welcome!!!!"Edited: 26 August 2021, 16:35
Bug Light Park, South Portland. There are picnic tables here and we've done carry-out with our dog here. There is a boat ramp here and I've seen some dogs jump in just to cool off, but not really a 'swimming spot'. Great field for a game of fetch or catch.
Fort Williams - Home of Portland Head Light; great off leash area in the back of the park. Great vistas. Great food truck for lunch.
State Parks - most of the state parks allow leashed dogs. (Specifically Two Light, Wolf's Neck)
Gull Crest Field, Cape Elizabeth. Nice residential area park with forest trails and marsh boardwalk.
Quarry Run Dog Park: City of Portland. Fenced dog park.
WARNING: There is currently toxic algae at Hinckley Park (South Portland).
Two Light Lobster Shack (Cape Elizabeth) We've been there many times with our dog.
I've heard that 43 North (South Portland) is dog friendly at lunch on their patio. https://www.north43bistro.com/ I have not confirmed this, but my neighbors have talked about it. You might want to call and ask. (It's a great restaurant!)
Snowsquall Restaurant (South Portland) has a patio. I've seen dogs there before.
C-Salt (Cape Elizabeth) has a patio. I've also seen dogs there. Note that this is a deli-counter service and not a full wait-service location.