If you want your site to appear in search results make sure you have not selected Request public search engines to not display my site
You can request how public search engines treat your site.
Note: This option is only available if "Anyone on the web" can view your site.
- In Google Sites, open your site.
- At the top, next to "Publish," click the Down arrow .
- Click Publish settings.
- If do you not want your site available in public searches, click Request public search engines to not display my site.
- Click Save.
Use Analytics with your site
https://support.google.com/sites/answer/97459