Welcome marktun and JIvories!
The trip from Plymouth to Providence should be a good shake-down cruise, and it could be done in a (long) day. However, IMHO, you would be better served to do it in two.
Getting out of Plymouth will likely take more than an hour. It is a long slog to G "1" Q G BELL
, which is where you will finally be out of Plymouth Bay. Be careful, and stay in as there is always shoaling outside the channel. From there it is a short hop to the Sandwich entrance to the canal. If the tide is with you, go through. If not, spend some time at the Sandwich Marina, waiting for the tide to change, and making adjustments to the boat. If needed, you can get repairs here too. If you spend the night, in Scituate, get up, and head through the canal EARLY. If you go straight through the canal, plan to stay overnight at Onset, or Red Brook Harbor.
My advise is that you NOT attempt to transit Buzzards Bay with a new to you boat in the afternoon. Also, be sure that your motor is working well, because you will likely want it to help here. The wind in Buzzards Bay usually kicks up large swell in the afternoon. If there is a steady breeze from the southwest (and there usually is), you could easily be heading through at 10' swells, and will be doing the "Buzzards Bay Bash." It makes for a long and uncomfortable day. Fortunately, there are lots of places to bail out if conditions get fugly.
I suggest that you forget about Westport, as it is at least an hour to get in, and another hour to get back out. Gooseberry neck (and Hen and Chickens) will seem to take an eternity to pass. Also, unless the sailing is great, I would skip Newport, and head up the Sakonnet River. Once you get past Sakonnet point, the river is wide, and you can usually sail either a beam reach, or a run right up the river.
I keep my boat in Barrington, just a little further down the Providence river than Providence. I could care less that Block Island, and Cutty Hunk are a full day away, Narragansett Bay, the East Passage and West Passage, and Mount Hope Bay are great for sailing when the conditions suck in Block Island Sound.
PM me if you would like more info. or assistance.