Rank a subdomain

It can be done but only if those other pages have unique content specific to those areas. Simply regurgitating the same info and substituting the city name on each page will not cut it.

It's tough to get ranked for other cities because G wants to show the most relevant result for their searcher; in other words, if your business is in Cleveland, Ohio, it will be difficult to get ranked in the city of Parma, Ohio.

If, for example, Parma doesn't have any/many of your competitors, you would have a good chance and optimizing a page spelling out you service Parma, Ohio could do the trick because G has to show something in the search results.

If you have reviews/testimonials from customers who live in Parma, Ohio, for example, title a page or post like this: Mary Jones from Parma, Ohio, bla bla bla.
G may pick up on that.

Here is another trick I use that works:

Use a directory plug in and actually list your competitors located in the city you want to expand to.
Sounds crazy, I know, but it can work, especially if you have good, useful content on your site. Put it this way, you're not ranked there anyway.

Your giving G just what it wants; content plus listings of businesses for the local searcher.
Search any local type search term and several directory listings are always on the first page of the SERP.

After the directory page gets indexed, wait a month or two than delete the contact info just leaving the name of the business with a clear, click here button that takes the visitor to your home page.