Your UNC club entry is coming up high in the rankings:
www.unc.edu/bellttmi/
Also, you have some competition because of the club, "Chapel Hill Toastmasters"
What you need on your club website is some basic Search Engine Optimation to let Google and the other search engines know that your website is definitely about Toastmasters and Chapel Hill. Fortunately, for a TM club, that is straight-forward.
The first, and easiest, thing to do is to put "Toastmasters" very close to "Chapel Hill" (no quotes) several times on each page you can change, and it needs to be in sentences, not in a bullet or numbered list.
Here's some examples, try other ideas too:
Bell Tower Toastmasters in Chapel Hill is a friendly club where you can build your communication skills.
We are the frendliest Toastmaster club in Chapel Hill, NC.
I also suggest you drop the numbers on the four numbered lines, and weave more references to Toastmasters and Chapel Hill in. About three times a page is good, but don't put them all back-to-back.
On the directions page, also work in a couple of sentences with Chapel Hill in the same sentence as Toastmasters.
Other ideas: Set up a Google My Business entry if you can. In spite of the name, non-profits can use it too. The only challenge is that they want to confirm the address, so you will need to figure out how to get a postcard delivered to that address for the confirmation.
Implement some of these ideas, give it a week or so, then try your searches again and see how you are doing.
George