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 is something they support, albeit in a buggy temperamental roundabout way.
- They are capable of outputting vectors - so in the resulting file you can select each individual path, road, icon, contour, label etc and edit each one independently, and scale the chunk of map to any size.
- Their license (Creative Commons Attribution-Sharealike) explicitly allows this sort of thing including for commercial work, so long as they're credited and you share the work you make with their data under the same licence, whereas Google are strict about usage of their maps unless you pay for an expensive license.
The downside is, as is often the case with open source stuff, it's not slick and takes trial-and-error to get it all working. There seems to be four approaches (the first three are further detailed in the above guide):
- Use the free software Maperitive (Windows software that requires a dependency to run on Mac/Linux)
- Using the expensive ($1399!) Illustrator cartography plugin MAPublisher.
- (the one described on the linked page) Using a Perl script that removes all styling and text: not easy to do and probably not suitable if you want something quick and simple.
- Exporting as an SVG or PDF file, using the Export button above each map view, then cleaning the file up (details on how below). Note that this is buggy, it sometimes fails with an error message about there being too much load on the server, but in my experience it usually works a few minutes later. There might be different times of day when it is more reliable.
SVG via Inkscape
Illustrator has some issues with the SVG files OSM produces (see below). You may be able to sort these out by opening them in the free open source Illustrator alternative Inkscape, then exporting for Illustrator. The only problem with this plan is, Inkscape like much open source software is temperamental (doesn't work on my Mac at the moment for mysterious reasons), but if it does work for you, this might be easier than fixing the SVG in Illustrator (below).
SVG in Illustrator
The labels can go a bit crazy in the SVG files in Illustrator - sometimes turning into a big mess of colour that turns out to be a jumble of giant letters:

These can be cleaned up by deleting everything in the Symbols window (select the first one, hold shift, select the last one, click on the bin icon in the bottom right), and choose 'Delete instances'.

Then, inside some groups and clipping masks, there's a whole lot of expanded-text non-editable-text labels with white outlines.
- If you want to wipe these out and add your own labels, select one,
Select > Same > Appearance, then delete.
- If you want to keep them but make them look normal,
Select > Same > Appearance, set the fill colour to 'Black', and in the Strokes window, set the stroke to 'Align stroke to outside' (or alternatively, in the Appearance window, drag the 'Fill' box above the 'Stroke' box).
Select > Same > Appearance might miss a few types of label, so check, and if it does, use the same trick to get all these other types of label.
Here's the result, a cleaned up, 100% free and legal to use, editable vector map of any location in the world:

PDF
PDF export is temperamental like SVG.
In my experience with PDFs exported from OSM, there is a heap of strange boxes that need to be deleted, then below this the text labels are real live text - but in Illustrator these labels are completely garbled boxes, even if you change the fonts, with non-text white outlines behind. (in seemingly everything except Illustrator, including Acrobat, they're real text without any problems).
I generally use SVG and add my own text, but there might be some way to salvage the PDF labels I'm not aware of (or it might be a glitch that will get fixed). Programs other than Illustrator seem to cope with the PDF just fine, so the problem seems to be more with Illustrator than the PDF itself.
If you can find a way to stop the text turning into , this will probably be the best method. Installing the fonts used (DejaVu Sans, free) might do it.
Maperitive
The best other option looks to be using the free software Maperitive to export an Illustrator-compatible file, see this guide. I haven't tried it because I don't fancy installing all the dependencies on a Mac, but they're all free, so if you've got 30 to do and not much time it seems like a good bet.