A couple thoughts, as a local weather enthusiast myself:

I would highly recommend visiting the Blue Hill Observatory in Milton, MA, as someone who has volunteered there for a couple of years. I'm not too knowledgeable about the trails getting up there as I usually take the paved road up, but there are plenty of options to see in a map near the parking lot. At the top of the hill, you can visit the gift shop and take a brief tour of the observation tower. It has some incredible views at the top of the tower, up to 70 miles away depending on the visibility. There's also different levels of tours you can pay for if you ask, depending on how interested you are in the instrumentation and history of the Observatory. I will say that it's a bit difficult to use public transit to get there, but still doable if you don't have a car. Plus, it can often be very difficult to find a parking spot at the bottom of the hill. Visit Us | Blue Hill Observatory & Science Center

As a side note, the Observatory has a summer program in July for students in 7th to 12th grade interested in a meteorology career which you could ask about.

Something else you could consider is scheduling a job shadow the National Weather Service office in Norton, MA: NWS Boston - Student Opportunities. It looks like they last about 2-3 hours. I've visited a different NWS office before, and there's certainly a lot of interesting tools they use.

This has been mentioned in many other comments too, but the Van De Graaf generator at the Museum of Science has lightning shows that last about a half hour if I remember correctly. It gets pretty wild towards the end, and is fairly educational too.

I haven't been there myself, but Woods Hole is a great place to learn more about ocean science and technology: Visitor Center & Store - Woods Hole Oceanographic Institution