Michael's Church (oldest section from 1070), and the site where the Mayflower and Speedwell sailed for America in 1620.
Walk along Above Bar Street towards the waterfront, and you will see the Marlands shopping center on your left at the junction of Civic Centre Road; then West Quay Mall on your right.
The latter is the newer, bigger, high-end mall housing large stores, such as John Lewis, Waitrose and Marks & Spencer, plus a number of specialty shops and boutiques.
There is a coffee shop and gift shop on the ground floor selling all sorts of Titanic-themed stuff; and adjacent is another room which houses temporary exhibits..
If you are keen to learn more about the city's Titanic connections, there is a walking tour leaving from the museum that takes in memorials to the ship's musicians and engineers, none of who survived.
When you leave the museum, head for Above Bar Street to the Titanic Engineer Officers Memorial in East Park (opposite the Cenotaph).