Since I live in Arlington and do not go into Boston, you'd think I'm pretty much unqualified to offer an opinion.
Regrettably, though, that doesn't stop me.
I think if I were in the OP's shoes, I'd drive Route 2 to somewhere in or near Acton, take the commuter rail into North Station, and walk from there to State Street or wherever.
As others have noted, the drive into Boston on the Pike in an excercise in terminal frustration. Unfortunately, eastbound on Route 2 in the morning anywhere east of Acton is just as bad. Ditto 228, either direction from about Route 3 through the Pike. Which pretty much eliminates the alternatives.
Trying to get to Boston between 7 and 9am is going to suck. I would not drive if you need to arrive between those hours.
Here are the options I'd consider:
Drive to Grafton MBTA. Parking is $4/day.
Train leaves 7:10am arrives South Station 8:21
Train leaves 7:37am arrives South Station 8:56
Leave SS at 1:55pm arrives Grafton at 3:11. Many later options if you want to stay later.
Drive to Worcester Union Station. Parking is $14 (fourteen dollhairs)
Same trains as above, but they leave 13 minutes earlier.
Express train leave Worcester 8am arrives South Station 9:06am
Drive all the way in.
I'd plan to arrive by 7am or the traffic will suck. Meters are free until 8am (I think?), but many have 4 hour limits. If you get there early you might luck out with a meter. If you ever need to arrive after 10:30 driving won't be too bad. Arriving between 7:15-9:30 would drive me nuts.
Driving OUT of Boston on the Pike is a pieces of cake if you leave before 2:30pm. 1pm will be fantastic. After 2:30 pm it will get progressively worse. Leaving after 3:30pm would suck.
If you get stuck with a parking garage it will be expensive.