What's the best way to change from careers in finance?

I am currently doing entry-level finance-related accounting work in NYC, but do not hold a degree in Accounting (just your standard BA from your local not-nationally-recognized college with a lot of finance classload). I really want to get into more of a research analyst position, or something more to do with the management of securities for some type of fund. How do I get my foot in the door?

As you probably already know, entry-level is key when entering a field for the first time. You are at a good start right now, but know that reaching the level of a research analyst or securities manager is not a quick ladder.
I would suggest attending a local chapter meeting of the CFA Society (Chartered Financial Analyst) or CFP group, network with a few individuals and ask questions.
For job opportunities, check with a bank (Bank of America, Bank of New York) or securities firm (JP Morgan, Merrill Lynch) and even AXA Advisors, for entry level positions such as portfolio manager assistant, investment assistant, or research assistant. Remember these types of positions are highly competitive.

Start honing in on your skills, read up on the securities industry to see where you want to be.
Good Luck!