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Assuming there isn't a reason why it has to be the Google-copyrighted maps you use, I'd use OpenStreetMap for this (the open source wikipedia-style Google Maps alternative). They're virtually identical but with three clear benefits in this case: They have a step-by-step guide on exporting to Illustrator. There isn't a simple process (more below), but it ...

Start with a very high resolution raster effect: Maybe 1200 ppi. Apply a slight blur to eliminate any evidence of aliased pixels. Spend some real quality time with the multitude of variables in Illustrator's trace settings. You can make surprising changes with small adjustments. And don't forget that this is low tech effect.

Draw your box filled with your pattern over the artwork. From here you have a couple options: This assumes your pattern has "holes" in it and is not a solid-filled pattern. Select all and click the Make Mask on the Transparency Panel. You may need to uncheck the Clip option on the panel or check the Invert option on the panel. Select the pattern box and ...

Styled Maps Wizard ( link ) does the job. It does have a pretty good instructions that show up when you open up the website. Those instructions can be accessed at any point with the help button at the bottom of Map style panel ( shown in the image below ). Beloware the styles I used to create the static map on the right and in this link.

If you're using it for a logo, then you're probably being paid enough to clean it up by hand (using the ellipse tool). Or, do it the smart way, and just get the Phantasm CS plugin, which has a vector halftone feature. If you want to reproduce the Photoshop halftone filter, you need to start by getting the grid angle and DPI correct. Then you just need to ...