Don't avoid cold calls. I started doing web development for myself almost 3 years ago and I was able to support myself and then was picked up by a much larger tech company in Chicago. I work at both now and this is how I made it:
Did one free job for a local small business. I sought them out. I just called, told them honestly that I needed to start a portfolio and offered them a free site. I did it quick, on Wordpress and used the experience to gauge how much time and effort a typical site would take and I based my first fees off this.
I wrote down names of businesses around town that I came across then looked to see if they had a website. Amy time I saw an awful website I'd contact the place and sell myself. At this point my rates were so low they might as well have been free and I bagged a few clients.
After I got about 4 sites under my belt and on my portfolio I raised prices, offered web app development and marketing and then joined a local group of business owners that met for lunch weekly. I made connections there and at various networking events held by local chambers around the Chicago suburbs.
Through these connections I got a few more clients. Once I got to job six or seven I tripled my rates and the strangest thing happened. I got less leads but the majority of the leads that came to me we're eager to close and easier to close. I was working less to close deals and those deals were worth three times as much as before.
I then slowed way down on reaching out to prospective clients as I had a steady stream of them contacting me first. The last group I contacted was a new non-profit in town whose cause was something I related to. They paid for my services and asked me to join their board of directors after I finished their (now "our") site.
Through that I made connections in the non-profit sector, state and local government, and with lots of people in the medical field.
I bumped up prices a bit more and saw an opportunity. Until then my market was anyone who wanted a website. Even though I weeded out a lot of the crappy clients by increasing my price I still got a lot of awful people to deal with. So I then focused in on non-profits, government, and social services (which was close to what all the connections I made in the medical field were into).
I'm three years in, work for an awesome and growing company, and my own freelance work is booming. I make a minimum of $2k for a run of the mill business website.
Things to note: throughout that time I used AdWords (about $400 worth of Google's free gift cards in total), I had a website from day 1, and I forced myself into lots and lots of social situations that were awkward for me. I also made sure I was on Yelp, Google Places/Maps, and every business and/or web design directory I could find.
It's important to know your market too. Where I am, even a halfway decent designer can look like a genius because all the local design firms create sites that look like they came straight out of 1997 GeoCities. I've had multiple clients turn to me after being pitched by them. I'm not a great designer either. I'm so-so. You can see for yourself how truly unimpressive I am at https://chooseclever.com. I'm not awful but I'm not above average by any means. Is your competition great? If so then do you compete on price or quality?
One thing I've learned along the way is that most everything you read about clients in different web design blogs is true. Same with pricing. I didn't listen and had to learn the hard way.