This may seem a little off kilter since I can’t think of any locations at the moment, however; have you considered maybe a food truck-style coffee shop? If not, I’ll just plant the seed in your mind.

But I was thinking maybe West End, but that’s also in Providence. In EP, you could try by city hall or the HS, but those areas seem too busy for good foot traffic. Most places that come to mind for a good coffee shop are in Providence, either near the East Side or downtown, but all of that goes against your stipulations. :/