Noon is a good time to go. You aren't going thru Manhattan anyway, so no worries about city traffic.
Google Maps says fastest route to downtown Providence is 3 hours, which is I-95 all the way. If you want to stop to eat, those two places are fine, but you will be there more for lunch than for dinner.
If you want a more leisurely drive, Route 1 parallels I-95 and is very pretty in some parts, and very commercial in others, with tons of stop lights and town centers, etc. You will see beaches on that route, as well.
Heading back to JFK you will hit traffic on a Friday for sure