Hi,
Any recommendations on which software to use to create encounter maps including zones. I was looking to have maps similar to those on page 299 of the core rule book.
Well, paint? 
I’d say have a look at LibreOffice Draw, Inkscape, GIMP or mtPaint, not necessarily in that order. While Draw and Inkscape create vector graphics that can be scaled infinitely without loss (and, thus, will print nicely), GIMP and mtPaint are ‘classic’ pixel-based image manipulation softwares. Both GIMP and mtPaint support layers (which will be neat when working with zones as you could hide them with one click), but GIMP is a relatively mighty software more comparable to Adobe Photoshop than to paint while mtPaint is… well, more like Paint. 
Since you want to create maps that are, in essence, geometric forms and some lines, I’d recommend to first look into the two vector graphics softwares (Inkscape is probably the more professional approach, I think) as you should be able to create polygonal shapes that can be modified any time while not needing an abundance of filters, effects and stuff.
All of the software I mentioned is free and open source and should work regardless of your operation system. Good luck with your first map(s) – feel free to share them here in the resources section, I think.
This may be a somewhat unsatisfying answer, but essentially it comes down to this. I use Sketch for Mac which costs money, but I have several projects where this is useful, so I get a lot of milage out of it.
Most of the work comes from creating the assets. But if you have your transporter platform, consoles and some rooms setup, you can re-use everything.
I actually copied the sections I needed from the few example maps in the books. Zones are just dashed lines, so pretty easy.
Any thoughts on how size zones? or is it a best guess?
Interesting, could you do a short walkthrough on how you use it for STA?
I prefer to think of zones in terms of terrain, not size. Elevation changes, barriers, or bottlenecks mark places where a zone boundary can reasonably fall. A simple example is a transporter room with an adjacent corridor. I would define the main floor of the transporter room as a zone, but the transporter platform becomes a separate zone because the elevation change draws some mental attention if you’re going to barge onto or off of it. The corridor is at least one more zone because the door impedes passage at least momentarily.
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Thanks everyone.
I use it for anything: Tokens for online play, LCARS-style sheets (I modified the STA bridge officer sheets to fit the TNG roles), maps, etc.
The feature I use most is re-using components as symbols. So I can also create custom cards for other systems, such as Savage Worlds.
I just use a dry-erase hex-grid board…
You simple country doctors and your dry-erase hex-grid boards… 
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