Are small dogs welcome?

I doubt inside the museum but yes on the grounds.

Not inside the museum.

Only outside the museum, unless it is a service animal.

I don't think they are allowed in the museum. They may have an exception for work dogs. Dogs hiwever can run around outside. I believe they have a dog park in Centennial Park.

Only the smallest and cutest

And

Not unless it is a valid work dog.

No, not inside the Parthenon... but they are welcome in Centennial Park on a (no longer than) 6' leash.

Park yes but Parthenon I'm not sure.