I think you planned well. MHT will be easy to get out of on Thursday afternoon for your drive to Danvers. Also, very easy to get back to and out of MHT on Sunday afternoon. MHT generally has much shorter security lines.
My choice for Friday afternoon - if you don't have a ton of luggage - would be to drive west on 128/I-95 to I-93. South on 93 about 7 miles to Route 16. Turn left at the offramp stoplight and go roughly 2 miles to route 28 (third stoplight). Turn right onto 28 and take an almost immediate left (75-100 yards) into the very visible parking garage. Take the short tram ride to the T station (Wellington Station of the Orange Line).
Take the "Inbound" T train about 5 stops to the State Street station. Follow signs to the Blue Line (within the same station) and go "Outbound" one stop to the Aquarium stop. Ascend the escalator and go east on State Street about two blocks to your hotel.
On Sunday you can reverse the process.
You can get more T info (maps, frequency of service, etc.)
here