I performed a free analysis for our friends at Zion Lutheran Church, School, and Child Care in Corvallis, Oregon. As a website builder, I did not try to sell them a new website, since the school and childcare website was just fine. The church website was a Google Sites creation that functioned fairly well and was considered to be mobile-friendly. No sale for me, right? Yes and no, since a church's online presence is more than the sum of the websites.
A Google Site is almost never going to seem top-of-the-line. I would mention this to Zion Lutheran, but, as I said, it was not a bad website, so I'd probably just recommend trying to get it to fit better with the school and childcare, both of which are serviceable WordPress websites. I'd ask Zion if the goal is to separate the three entities or tie them together, since all of the websites appear to be unique and different. That's not a criticism--just an observation, and it might be exactly what they're going for. Since I can appreciate the ease-of-use of WordPress and the freebies available for Google Sites, I'd probably try to embed most of the main church site into a WordPress template that will also be used for the school and childcare, trying to save the best Google Sites tools if they are used. That said, when I did a Google search of schools in Corvallis, both the school and church showed up nicely, meaning the staff is doing an excellent job with content.
Your web presence is not just about your website, which I found out while initially searching for Zion. Google Maps had Zion Lutheran Church listed as a Baptist Church. While I suggested an edit and had this fixed, how long had it been listed with other Baptist churches in Oregon on Google? Church members don't often step back and search for their own church, but remember that non-members are searching all the time. I did not have to have or set up a Google+ page in order to suggest an edit, and Google had it fixed in a day or so.
Another method you can use in order to improve your church's online presence is to add photos to both Google and your own website. Why Google? When people search on Google Maps, they expect to see a full tour of your church, not just the street view. When people search using Google Images, however, you'd like for the images they find to direct them to your homepage, not Google+, so you really need photos in both places. And photos on your own page should be indexed properly with Google, as in using a sitemap, having an appropriate filename, and using alt and title tags. I like to add images right to content (like this article) rather than use an image gallery if I want the images to be found by search engines.
I've discussed content a lot on Luthernet, but the last way to help your online presence is only partially about content. It's about links: adjust them and create them. If a website that mentions your church is not linked to your own website, see if you can add a link. If it has reviews, see if you can add one of those, too. Use Google to see what non-members would find, and then go to each website. If you want better linked pages, then create them. Luthernet uses its network of websites in order to create articles that link out to websites we build, but you can ask church members with business websites to link to you. Or a local government or tourism page. Or use Facebook. Every link helps a little, and there is no reason to run away from free advertising. Be aware that people who have been disappointed with your church will use the internet to post a review at some point, but that does not mean you ignore them. Instead, ask three others to post perfect reviews. With Zion, I wrote a few articles about the church that will provide links and relevant information that will come from several domains. Luthernet sees your success as our success, so we try to drive traffic your way if we can.