Igreja Matriz Nossa Senhora do Rosário is a beautiful church near the museum. It is sometimes open in the mornings. You can see the spires from most places in the city. It's a good starting point for exploring the city.
Museum of Hansen Bahia- The museum is on the street behind the church. Hansen Bahia was a German artist. He visited Brazil and loved it so much he made it his home. The museum has a lot of his art and it's free to look around. Visit in the morning because it is sometimes closed around noon.
"Sisterhood of the Good Death" Irmandade Da Boa Morte - If you're interested at all in Candomblé, you can get some information here. The sisterhood was originally organized to ensure proper burial of members of their religion. Looking around the one room is free but they will ask you for donations. It is located across the street from the Hansen Bahia Museum.
Dannamann Cigar Factory (In São Félix) - Tobacco has been grown in this region since the 18th century. Dannamann Cigars are considered the best in Brazil. Even if you aren't into cigars, you can watch them being made and it is very interesting. The "showroom" has free coffee and you can buy cigars and smoke them on site. It is located across the bridge in São Félix along the river.
Visit the Market- If you arrive on a Saturday morning, you can get off the bus in the market. Many Brazilians do their weekly grocery shopping at the market on Saturday mornings. There is a lot to look at besides food and it’s a great cultural insight.
Learn about Candomble - If you ask the right person, you may be able to observe one of their meetings. It's a fascinating religion with roots from Africa.