In a way, you're thinking too much like a brick and mortar business. :) Restaurants, mechanics, dry cleaners, local grocery stores, chimney sweepers, painters, and other jobs and businesses that require on-site presence don't scale very well beyond the borders of their town or city.
However, as a website developer, your services scale beyond the city limits or the town borders. With technologies today like Google Hangouts, Skype, and other forms of online communications, you can meet with many of your clients remotely, without ever needing to physically step across their threshold.
Likewise, we live in a world where people seek the Internet when they look for a vendor. Therefore, you'll be much better served by having a website of your own and a blog with articles that reach out to the prospective clients you hope to seek. As an example, my first client was in New York while I am in Oregon.
Also, attending networking events and conferences that your potential clients may go to may also prove helpful. Sometimes, you can find free events you can attend, which helps with your budget. Depending on the event, you may meet people with global connections, and this may have a much stronger impact than becoming a 1950's door to door salesman. :) A person I spoke to at one of these events knew the company he worked for needed someone with my development knowledge, so I landed the contract thanks to his referral!
Lastly, consider that many businesses who don't have a website may not actually benefit from having a website. In a world where many local businesses are found on Yelp, Facebook, or other aggregate sites, the value of a website may not be all that great or desirable to them. Then you must consider whether or not these businesses have enough revenue to justify the expense of paying you a decent fee. In my experience, it's better to target businesses that have a more global reach, as they'll more likely have a need for a more global presence on the Internet and also have enough income to pay you what you're worth.