How do I make my website show up in Google search when searching by city?

I want to make my club website show up on a Google search when searching by a city/state, as in search term "boulder toastmasters"
My club is in Boulder, Colorado. I want searcher using the search terms "boulder toastmasters" to come up on the search.
Club name: Loquacious Lunch Bunch
Club number: 7329

You have NO, ZERO, NADA, text on your home page search engines cannot read pictures.

If you want the search engines to treat you nicely you need lots of pertinent text.

Answer the 5W and How on your home page in text.

What Brian said!

In addition to redoing your home page as text, add a couple of sentences that link Toastmasters and Boulder.

For example, here's one example:

Loquacious Lunch Bunch is one of the friendliest Toastmasters clubs in Boulder.

Do the same thing on your directions page, putting Toastmasters and Boulder in proximity

One other thing: Google ranks websites higher when they have several links from other (legit) websites. It appears that your club has a Facebook page, but it does not have a link to your website, instead it has a link to a broken page on the D26 website.

Change that link to point directly to your website.
See if some of your members will also add links from their social media pages (FB, LinkedIn etc) to the club website.

One lastthought: do that Google search on "boulder Toastmasters" and then study the club websites that come up. Learn from them, adapt some of their ideas to fit your club.

Besides what others have said, in the admin area under Basic Settings, you need to place keywords in the keywords spot of how you want people to find your club on Google and the other search engines.