Question: My site is currently structured as such: city.example.com/
To improve my Google rankings, should I restructure it as such:
www.example.com/city/
I believe it will eventually help for BL's...but are there any other advantages?

Answer: It actually depends on what you're doing with your site. For example, if you host several different "themes" on your domain example.com, I'd create a sub domain, b/c as we know, SEs see them as a separate site. That way, city1.example.com can contain 1000's of sub folders/pages pertinent to city1:

EXAMPLE #1
city1.example.com/events
city1.example.com/dining
city1.example.com/recreation

But, for example, if you have:

EXAMPLE #2
www.example.com/city1
www.example.com/dog-grooming
www.example.com/classic-cars

You are now not capitalizing on the ability to create keyword-rich URLs, as you can do with creating your sub domain (IE: dog-grooming.example.com
You'd then consider each sub domain vs. domain.com/sub-folder as separate sites, and work on separate SEO strategies (IBLs, etc.) for them.

PS: Imagine your sitemap for EXAMPLE #2? It'll look like a link directory! As apposed to EXAMPLE #1 - which would show SEs the "theme" for your site.