I like some aspects of your site, but I don't believe you earned a 2nd page ranking for the target phrase. There is seemingly a lot of competition for the keyword. Many developers from around the world might create a "web design greenville" page and attempt to compete with you. Here are some suggestions:
1. Your home page title and header presently target two keywords: "Website Design & Graphic Design Greenville, SC". If you perform a Google.com search for "Website Design & Graphic Design Greenville, SC" you are the #2 result. Your title and header represent the phrase for which you wish to rank.
If the most important phrase is "Web Design Greenville SC" then change your title and header to match. You will likely notice an immediately improvement in ranking once the change is made and crawled by Google.
2. You do not have a single backlink to your site using the phrase as anchor text. While you don't want all your backlinks to use the phrase, some of them definitely should.
3. Add your physical address and phone number to your page. Saying you are providing service for Greenville in your header is not enough. There are tons of companies in Los Angeles, NY, Miami, India and the rest of the world who are offering similar pages. You have the advantage of being authentic. Leverage that advantage by publishing your information on both your home page and the About page.
4. Use your target phrase at least once in your content. "I have been providing Web Design to Greenville residents for 5 years". There are many other ways to present the phrase but it needs to be there on your page. Preferably 2-3 times.
There are other changes you can made but these four changes alone have a great shot at bumping you to the first page of results. At the very least, you will dramatically improve your ranking.