I agree with Akula's advice. I bet doing that will also prevent you from becoming overly dependent on the GPS and help you learn how to use the maps.
I'd also suggest learning as much about how the streets are laid out in your area as you can. Most places are set up on some sort of grid, and if you learn more about how the streets are numbered, named and such, you can start cracking the code and find where you're going much more easily.
Using this system I can easily find many locations without even looking at a map or anything like that. For example, around here we have a hundred-block system. A grocery store is located at 655 N. Main St. I know that the hundred-block for Main St. is 12100 E, meaning it is 121 blocks East of the 000 block, which is like the Y axis.
The address of the grocery store tells me where it is located on Example St... 655 means it's between 6-7 blocks North of the other 000 street, the X axis. I know that the 600 block is Something Ave, and that the 700 block is Example Ave. So I know that 655 N. Main St. is located on Main St. between Example and Something.
Since I have all of the major streets and their corresponding hundred blocks memorized, I also know where all of these streets are in relation to a single central location. Our city also follows NOW SEE rule - Odd numbered addresses are located on either the North or West side of the street (depending on which direction it runs) and Even addresses are on the the South or East side. 655 N. Main St. must be located on the West side since the street runs North/South.
Of course, this may not be how your city is set up, and there are always exceptions to the rules: roads that don't run through, crazy curvy roads and such. But most cities have some sort of rhyme or reason that can help you predict where an address or intersection will be. My suggestion would be to ask around and see if any of your coworkers are aware of such a system. I've also found that cops tend to be great resources for this kind of stuff, since they tend to be out on the street more than EMS or Fire and usually have excellent knowledge of local geography.