Take the resort bus to Hollywood Studios and transfer to the boat going to Epcot. Exit the boat at either the Boardwalk or the Swan and walk to the restaurant.
Or plan to go there after being in Epcot. It’s very close to the International Gateway.
Alternatively, walk to the MK bus stop and hop on a BWI bus. You can also take a bus to DHS and boat or walk to BWI, but this will be the slowest of all options.
You can also monorail to Epcot, walk through the World Showcase to the International Gateway, then board a boat to the Broadway.
I think this thread shows there are many different ways to get to the Broadwalk from the Contemporary so pick what works best for you.