Good question. I was wondering the same thing a couple of years ago -- I'd been working at a couple of start ups and felt drained and uninspired by my work and wanted to make a difference. I found Code for America which has job lists for public-good technology work, and through CfA I found a company called Nava where I now work. Nava partners with government agencies to build better, more usable, and more equitable digital services to replace/improve services that fall short of what the public deserves, especially for under-served populations who most need them. We do a lot of work on healthcare programs and veteran's affairs programs.

USDS and 18F are also both great organizations in a similar sphere of work. There's a real need for software developers who want to do good to help design good services, improve existing ones, and rethink poorly conceived ones that don't do their users justice.

Nava: https://www.navapbc.com/ CfA: https://www.codeforamerica.org/