Though it's arguable, the scriptures certainly tend to support the idea of door-to-door evangelizing. After all, how can you shake the dust off your feet at an unwelcoming house if you never approach any houses?
(Matthew 10:14) Wherever anyone does not take you in or listen to your words, on going out of that house or that city shake the dust off your feet.
I think it's a bit much to read door-to-door evangelism into that text. The fact that they might have gone to some homes hardly implies that they would pick a street and systematically call at every house. I'm not saying it couldn't have been that way, just that you can't make a strong case for it from the Bible.
Even if you could establish with certainty that the early Christians preached from door to door, that wouldn't mean that it is the best or only system to use today. Christians back then rode mules and wore sandals; things are different now. There are much more effective ways to spread a message than trudging from house to house, especially in a society where unsolicited calls at the homes of strangers have fallen out of favor.