Or could I go in, sit in a back pew and pray quietly and leave when finished?Not sure if your St. Mary's has Eucharistic Adoration (where Jesus -- the Host -- is in a Monstrance (not necessarily in the church proper) for the faithful to Adore; check here to find out), but it doesn't matter as Christ (the consecrated Host) is in the Tabernacle (little box behind the altar or to the side), which brings a wonderful peace to the church. Anyway, one does not need to believe in Christ (who would know?) to enter the Catholic Church, and one certainly does not need to be Catholic either.
Of course I know Christ.
The church lists “perpetual”
so I assume that means the doors are open to the chappel 24/7?
Thanks for your info.