What's the best way to find local clients?

Your local Chamber of Commerce is one of several opportunities to connect with new clients. Also such organizations as The Rotary Club, Linqs, are also good options. Business mixers are good locations along with bartering with some of those business for their initial business to get your reputation and name out there.

Go on zip recruiter and put in customer service you will find tons if sales and marketing companies. Most marketing and sales companies grow at a fast rate so they need people who can make their websites stand out from the competition. Also make a website for your self to showcase yourself and your work and go to these business. Nothing can beat face to face

I highly recommend Facebook ads and a retargeting pixel on your website.  This allows you to target the perfect customer demographic and display your ad to them repeatedly after they visit your website.  It's one of  the most effective ways to get more customers calling within a week.   Then you can tweak the targeting and let the FB magic algorithm do it's thing 

Do you really need local clients? My digital marketing agency has NO local clients and all our staff and clients are from around the US (and the UK too!). I can show you how to attract this kind of business if you are interested.

I understand,  I have lived here my entire life and I still struggle with that sometimes. I find naturally talking with folks in shopping lines, Lowes and other places we find opportunities. They are all around you and sometimes it takes a bit of luck. There is a small local radio station that you could advertise with called WIXE and they can help spread the word. 

Finding local customers is really about making yourself known in the community. For example a store owner who only stays in his store will get less customers than one who goes out to lunch at various local restaurants and meets the owners there, or attends rotary or other networking meetings. When you see people face to face you have their attention. If you talk about "them" not yourself( at the beginning) you have their interest. You can't break down new barriers by walking into a place a saying "Hi my name is Bill, let me tell you about myself and my business!" How would you react to someone who did that? Not with open inviting arms. However try "Hi My name is Bill I just moved in down the block. You have a real nice place here. How long have you been in this town?" You got his attention. He talks and then he is almost obligated to ask you "so what do you do Bill?" Now you've got him. That is the beginnings of a business conversation. 
This technique can be used almost anywhere. In my business one thing I do is to knock on doors. If you have something interesting to say its really hard to hang up on you when you are standing there face to face. I hope the thoughts help. Good Luck! Elliot

the local newspaper has a “real estate transactions “ section giving home sales with addresses and buyers names. Mailing directly with a discount for their first visit is very effective 

Before you try to find ‘more’ local clients, take this step seriously and take the time to do it right. Can you describe and define your ideal client? Do you know where they live and what type of car they drive? Do you know what’s really important to them regarding the benefits they get from using your product or service? Do you know what they find challenging about using your product or service? Do you clearly communicate what’s truly unique about your business compared to your competitors? KNOW who you want as a client (and why) first, then you’ll better understand how to attract them.  

I would say it's very similar to Real Estate. You have to network your but off. Focus on developing new relationships and treat it a large portion of your job. Networking is a skill. I see some people hit the ground running without missing a beat. Others it takes longer. Ultimately I always think it's important to make a decision to step out of your comfort zone and stick to that decision. It will pay off in the end.

Recognizing that web/graphic designers are a dime-a-dozen and you're invading the market zone of long-established competitors who want you to fail, there's only one (1) guaranteed way to find local clients.

Get some business cards and a laptop and go door-to-door showing your portfolio, which needs be much better than the other designers (a measly 10 years puts you in the minor league at best). No matter how good you are, finding clients is all about marketing. So you need to hustle on sales every spare minute.

There's an endless array of ideas to advertise and promote yourself, networking, cold-calling, etc. etc.. The fact that you don't know this, and you're asking advice on a such a lame platform as Alignable, doesn't bode well for you. You're lucky I gave you the only hope you have. Good luck and godspeed!