I am looking into doing an MBA to transition into finance but I have hit a major roadblock with the GMAT (580 - 38V + 33Q).

A friend of mine who did his MBA at Wharton suggested that my quant score would be important and I should study to get that up (as well as my overall score, which is also important). I haven't had much time for focused study so this has been a problem.

Nevertheless, I plan to at least apply this year. Is there any chance of getting into a good program with my current score?

Depends on the definition of "good" something like Fordham or CUNY could fit the bill, but for NYU, Columbia and the likes you'd have to prove outside of your GMAT that you are competitive.

Dear Ayon, thank you for the response. Do you think I would be competitive at Fordham or CUNY?

[quote]Dear Ayon, thank you for the response. Do you think I would be competitive at Fordham or CUNY?[/quote]
Write really strong essays. I think you'll get an admit - no scholarship perhaps.

Even though the avg GMAT for Fordham MBA says 622 and for CUNY MBA 612, it's just an average. You are in the ballpark.
Fordham MS programs mentions avg GMAT at 662 while my sister got admit with a 540. Of course since I helped her write essays, I like to take credit for all 5 of her admits, John Hopkins, Bentley, Kogod, Fordham and CUNY

Depending on the other parts of your application and your background, CUNY and Fordham might still be reach schools for you, especially with that quant score. If you could focus your study to address the weak points in the quant part of the GMAT, and get the quant score up closer to your verbal, that would help out a lot and give you a bit more headroom. Just getting the quant up to 35 or 36 would help you break 600.

I've scheduled another go at the GMAT. Hopefully I can get my score up!