In 2016, we ate lunch at Shack Shack/Chestnut Hill (same as the Star Market lot), left the car in their lot and walked to the stadium. I doubt it is encouraged to park there for BC games though.
Yeah, anything over $30 to park on BC property is robbery. So the safest bet is the BC Newton Campus (885 Centre St, Newton) for $30. Shuttle bus runs every 10 minutes.
I may just park at the Riverside MBTA station lot (367 Grove St, Newton). Take the Green Line D train to Chestnut Hill stop, and walk to the stadium. Parking is $3. I believe the train is $4.80 pp round trip. You need a "PayByPhone" account to pay the parking at an MBTA lot. (paybyphone .com) [If you've never used this before, I recommend that you set it up before you get there. You don't need the App, you just need an account.]
If you want stay on the train until the Cleveland Circle stop, you'll find some taco/Chipotle joints and a tavern. It is still walkable to the stadium from there.
If you rideshare, drop-off and pick-up is at Gate A of the stadium.
Back in the 80's I used to park on the street on Acacia Ave or Lee Rd, basically across the street from campus. Assuredly you'll be towed these days in that area.