From my perspective, you have 3 options:
- WordPress Multisite.
- 2 separate WordPress sites with a common landing page.
- 1 WordPress site with custom logic to determine content (store location).
Each direction has disadvantages, but each of them is possible and will result in a perfectly fine end product.
I cannot provide a recommendation. You need to determine the best course of action based on your comfort level, skills, and the needs of the client.