Have you considered taking the train (technically commuter rail) to Newburyport from Boston and then renting a car from there? It's quite close to where you're going and would probably allow you to avoid dealing with navigating the city in a car alone at all. You would just have to cab to north station instead, and could do the reverse when you come back. I also get some driving anxiety especially in the city (though less severe), and I totally understand wanting to minimize putting yourself in a more stressful situation than necessary.

If you're staying where I think you're staying, you'll be just fine. I live close to that area and my mom (who comes from Maine via Amtrak and is very nervous about "big city" traffic and public transit) has no problem getting around on foot and by T from the Royal Sonesta/ Marlowe block. That bridge also has a sidewalk that's very safe and leads directly to the TD garden/ north station area- I use it all the time to walk home even late at night, so you may find you don't even end up needing the train. If you do it's a newer and very nice little station, with the one quirk being both tap cards and tickets are validated at the ticket machines themselves, don't stress and just keep your ticket/receipt. The line leading there is also one of the quieter ones (E), if you hop on you can take it all the way to the MFA if it's rainy and you want your art fix or the Pru to do some retail therapy- I've been living in and out of Boston for the last 8 or so years and honestly I feel very lucky to be proximal to it, as it feels like one of the last remaining non-chaotic lines these days.

We live a few blocks from this place and go every few months for their tasting menu. Never disappoints, and their drinks are great as well.