Translation:The garden is open to the public today.
I agree that it sounds more like "g" than "dh". Thanks for the tip on Connacht pronunciation. When I was just starting to learn Irish, I was using a book in which the combined (inflected?) forms of "do" were actually lenited in spelling (eg dhuit, dhoibh). I don't know what dialect that was, but of course it's not standard spelling.
Sin an gairdín atá ar oscailt don phobal inniu.
"there" is a bit weird in English, and it is used in sentences with an indefinite noun where it isn't used with a definite noun:
Tá úll sa bhosca - "there is an apple in the box"
Tá an t-úll sa bhosca - "the apple is in the box"