There are several question embedded in your post -- the first and formost is how to build brand awareness. I will answer that. (The other questions about advertising and how to grow are great questions and deserve their own virtual real estate)
A geographic "home" is not neccessary for building brand awareness. Not one bit. It may be nice. But not needed. There are a variety of overall marketing stratgies you could choose. One is finding a demographic and securing support
In looking at your site and the cove value proposition I will reccomend the following:
Sponsor Stuff : Sponsor stuff at the St. Paul Saints game. I know that pig could use a sponsor. Sponsor a fantasy pitch game. Call them and talk with them about how to make sure that every single person who goesto Midway Field this year knows your name when they leave.
Think Youth Sports : Become a corporate sponsor but be active. Go to events and meet people. Network. Invite.
Niche market websites : Where do people who want to improve their baseball skills go online? You know because you are part of the community. Approach the owners of those sites and offer to write a guest blog, and bundle some advertising dollars in with the offer.
Leverage your talent : All of the ball players that are part of your instruction also sponsor events and nonprofits. Work with them to offer discounts to your school (underwritten by the player) as silent auction items at those organizational events. They need to provide stuff, and you need access to the prospective customers.
Social media your talent : Can you have each of your instructors shoot a short :20 second "lesson" which you post on YouTube and link to your site. Then everyone who loves and searches about that ball player will see their mini lesson and link back to your company?
Be sure to develop a good CRM infastructure so you can effective track your lead and opportunity sourcing by campaign so you can inform your understanding of what is working and what isn't. Once you have built some equity in the Twin Cities market you can develop a marketing campaign for replication into other markets.
A building, or "store-front", is only one way to announce your presence to a community.
Of course we have the well discussed social media components. You need a well designed, informative site that you can use to reach out to community members and groups. Facebook, Twitter, etc, these have all been discussed on this site.
Another avenue you may want to consider is to sponsor local events. Think of the age ranges you would want to advertise to (young adults and parents?) and find events that speak to them. Maybe public rec leagues, public safety fairs, etc. Become a sponsor of a United Way event that works with schools and family.
With this approach, one months worth of what you would pay in rent and billboards goes to doing a ton of good and getting your word out to your particular niche.