Would an addition of a sidewalk in front of a store front building be added to the basis of the land or added as a capital improvement on the building and be depreciated?

It would not be added to the basis of land. Land assets are considered to exist forever and thus are not depreciated. The land account should only include: the purchase price of the land, any fees or closing costs to buy the land, and any grading or clearing etc needed to make the land usable.

Because the sidewalk does not fit into one of these categories and because it does not “last forever” the sidewalk should be treated as a capital improvement and depreciated over the useful life. Also, it would be better to put it in an account like Land Improvements but I guess it would be okay to add it to the building asset account.