Yes they have a big parking lot, but on a sunday it wont be that easy to find parking. You should try to all go in as few cars as possible.
I normally go to Granola Bar on Sunday's and have never had a problem finding parking. I would go in as few cars as possible though just because the lot, though decent size it may be, still has a limit and shares the lot with other businesses in the plaza. Now an issue you may have Diane is waiting for a table. If you plan to attend with more than 4 people in your group, i would call ahead and reserve a table for your group on the seating list.
You can also park at Westport Playhouse, which is a five minute walk away
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