If they don't have it, claiming their Google My Business profile and optimizing it is crucial.
I think changing their page titles / title tags to include the keyword as the first word could be a very easy win for stubborn clients.
Embedding a map in a press release could help increase their GMB map pack rankings.
Create a new geographic location + keyword page for an area around the client's biz address, or all the surrounding areas if you can convince them to let you do that. (Identify what it is that the business offers. Check out their website to see if they effectively communicate that's what (and where) they sell. Identify the gaps (the missing info), then create those pages. Voila!)
Getting them hooked up with an SSL certificate so their site is secure, its quick and easy to do and proven to be a factor to improve rankings / help with trust.
On Page SEO can be done fairly quickly and shows them that you're serious about improving things on their site "the right way," they see you're serious and trust you more about doing SEO work even if they don't see results from it right away. For example, optimizing their H1 headings, meta title, descriptions, etc. You can also create more internal links to their important pages and reduce for the less important pages.
Fixing the client's 404 pages and broken links is something the client can see right away, and it can also be a great quick win that Google might pick up relatively quickly.
Publish a long tail keyword article for a topic they already rank for.
If they rebuilt their website and the web company didn't redirect pages, regain those lost backlinks. To do this you'd check inbound links giving 404, 302 and 307 server responses and 301 redirect those to a proper relevant page. Sometimes you can get new link juice from thousands or tens of thousands of links!
