Actual medieval towns were in fact very densly populated. According the the Magic Medieval Society book linked above (which is really a must have, go buy the thing!) a large town (which is where your population 2000 falls in the DMG) in the real world had a population density somewhere around 40-60 people per acre. Most medieval cities were smaller than 1 square mile (640 acres). The town should contain around 20-30 structures per acre.
Remember that everything in a true medieval city had to be within reasonable walking distance of everything else. Between cities, there are manors all along major travel routes. In other words, you're either within walking distance of some kind of settlement, or you're in the wilderness.
All this is based on real world data, and you're playing in a fantasy world. In my homebrew, I prefer things to be less dense, poor, and dirty than they were in the real world. As they point out in the DMG II, its sometimes better to design D&D worlds to reflect an anacronistic idea of how things were, rather than a realistic representation of the medieval period.
Still, its nice to have some kind of basis, which is where the Magical Medieval Society book comes in.