I work for a non-profit city-owned utility. Can I use these fonts to promote our energy saving programs?

Have a look to the read me file generally included with each font. In any case, contact the author to be sure.
Which font is it ?

Just any fonts. Sometimes I can't find the author. I try to avoid the ones that are not free for commercial use for this reason, but they are often good and I want them. So just wondering if font authors consider a non-profit a commercial entity.

Nobody here can answer this question about what the author considere as "commercial". Contact the author, it's the only one that can have a reliable answer for you. All other one can only reply with suppositions or speculations.

OK, thanks. I guess there's no easy answer!

Governments, including local, are (should be) by definition non-profit organizations and thus their utilities. But that doesn't make a font that is free for personal use also free for governmental use. Governments use these fonts to - in one way or another - communicate and that is professional use.
Mutatus mutandus; Not free.