The way to approach investors is the same regardless of location. Although there are many more opportunities on the coasts as I can attest being a serial entrepreneur here in Texas.
Before trying to approach investors, the first question you need to ask is: What type of funding are you really ready to raise? If you need intros to VCs, then my guess is you really aren't ready for VC funding but need pre-seed or seed funding which are areas that very few (and diminishing) VCs invest. If you are in the early stages of fund raising (i.e., this will be your first round of equity investment), then friends, family, angels, crowdfunding, and government sources are more appropriate.
Here are a few methods to attempt to get intros to investors:
1. Incubators/accelerators: Many incubators and accelerators have been established recently. Check to see if there are any available in your area to which you can apply. Here's one list of accelerators and incubators: http://webbmediagroup.com/list-of-incubators-and-accelerators
2. Pitch competitions: There are many business plan competitions across the U.S. The competitions not only give you experience in pitching your business, many investors are typically in the audience. Here's a good site on business plan competitions: http://www.bizplancompetitions.com/
3. Universities: If you are an alum from a university, then the alumni association can be a good source for introductions to potential investors. Also, if you have connections with a local university, then they may have classes and other opportunities to help with your startup, including investor introductions.
4. Friends and family: Many times, someone you know may have an investor connection. If they don't know you are looking for investors, then you may never know the type of connections your friends and family have. You don't want to come across as desperate or pushy, but casually letting people you know that you have a startup looking for investment may open up some doors.
Good luck with your pursuit for funding. If you are starting up a healthcare-related company, then I'd be glad to answer any additional questions you may have.