Abbreviations

Q. In running text, what is the preferred way to write “Washington, D.C.”?

A. Use commas:

Washington, D.C., was built on what was essentially swampland.

This recommendation holds true when you use the abbreviations recommended by the US Postal Service and now preferred by Chicago:

To me, Washington, DC, is first and foremost the home of the Smithsonian.

[This answer relies on the 17th edition of CMOS (2017) unless otherwise noted.]