Multi location pages for local SEO

I'm building a website for a client and they have one business address but work within all of the surrounding towns and villages. I wanted to create a specific page for each one of these locations with unique content to help personalise and benefit the person who lives in that town or village when searching the website.

Each one of these pages should have an address and a google map to help with local SEO but with only one business address i don't want to start duplicating content making it look like I'm trying to manipulate the search results.

So:

• Should I just avoid the address on each page and just use each location as way to highlight the benefits this company can bring in order to help with organic search?
• or should I just have one page that mentions all of these other locations plus all the benefits?

As far as UX is concerned I believe it would be better if each area had its own unique page.