The Silver line (bus that acts like a train) has a stop across the street. You can pick it up at Downtown Crossing. Otherwise, take the Orange line to Tufts and walk ~15 minute (3/4 mile) down Washington. Back Bay is a similar distance and Broadway is slightly farther.
I believe broadway on the red line and tufts medical center on orange are also both close
I believe the closest T Station might be Back Bay Station. That's about a 15 minute walk to the Cathedral. There are buses, but I'm not sure where you would pick that up.
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