You will likely have only driven around 150 miles by the time you finish the story. So this is likely to be a big grind. The best thing to do is head to the freeway (yellow road on map) and keep driving from one head to the other. You can get a good speed so will cover miles quicker. If you start running out of gas, just steal another car and carry on. Expect this to take around 10 hours.
There actually is a method of driving your vehicle through a clothing store. The car will break the display window and you will free fall through the bottom of the map. You can average about 30 miles every hour. Make sure to save your game often by changing the Subtitles in the Pause Menu. Also, it's important to note that you should save and quit the glitch when you have around 995 miles, and get the last few miles be legitimate means