Sketchup from Google is free. It takes a different approach to the drawing process than most drafting programs. There is lots of tutorial help. You will need it if you have any experience with traditional cad programs. It is a 3D modelling program vs. a 2D drafting program. I use it in addition to cad.
Autodesk has 123D available free.
http://www.123dapp.com/ Again, it is 3D based. I haven't used it, but Autodesk is the maker of AutoCad, the industry standard.
LibreCAD is totally free, open source software. Its feature set is somewhat limited compared to the big boys, but it is probably good for 95% of users.
http://librecad.org/cms/home.html
I've been a TurboCAD user since version 1.0 and it has worked well. The versions that are one or 2 generations behind are more than capable, and are less than $50 which is almost free...
laroke mentioned DraftSight, I'm in the same boat as him... downloaded it but haven't tried it out. Lots of tutorials, and their other products are industry standards.
I haven't used DeltaCAD in a while, but it used to be awkward, and really dated looking. Price is right though.
So, if you need .dwg or dxf files, then any older IMSI (TurboCAD) or DesignSight, or DeltaCAD, or LibreCAD will work for you. If you want to do 3D modeling, Sketchup is probably the way to go, given the online support (you can get 2D views out of it using the section tool.)
Given that most are free, try them out and find the one that matches your personality and needs.
Good luck,
zuk
(Just re-read your intended use, I'd go for Sketchup. That will give you views of what it looks like for the planning variance, and you can do sections thru the model to get floorplans.)