I would have done it all in GIS software (QGIS most likely) myself using shapefiles from the County/State/Town, but I suppose that depends on your preexisting knowledge of GIS software and access to high quality data. I

In order to look good, it would probably also require some substantial design work in the symbology of the layers you're using.

EDIT: Another commenter suggests OSM, and yeah, that would be way easier than starting with shapefiles for various features.

I use QGIS, usually importing an OSM-based vector map (look for the MapTiler plugin) and tweaking the layer appearance does it for me. I'm not 100% on board with how QGIS' print layout tool works, but I think that's just because I have a different model in mind. It's more print oriented, so it should hopefully work for you.

I have done this previously using http://maperitive.net/ to download OpenStreetMap data and exporting roads as SVG or AI, then using Illustrator or Inkscape to clean up and print. Maperitive is a bit clumsy and hasn't been updated for years at this point, I think, but it's free and worked well for my purpose (which sounds like exactly what you're trying to do).

The Stamen toner map may work well for you: http://maps.stamen.com/#toner/14/37.8024/-122.2645 Also checkout their watercolor rendering... probably my favorite basemap that I never get to use.

If you do use QGIS, you can get the Quick Map Services plugin that will connect you with these Stamen basemaps as well (and tons of other basemaps, a must-have plugin).

Stamen toner map is not that great for printing as it's still a raster.

Sure, I just mentioned it in the off-chance it was good enough out of the box. Big jump from making a screenshot (or perhaps stitching a few together) to editing OSM vectors in QGIS/Inkscape, which others have mentioned already.

mapbox studio will let you custom design layers, but i haven't gotten very far into it so i can't speak to the level of control you get.