Me too, but....
I've never been called a gringo (I'm black), this is neither positive or negative. i think Dominicans do see American blacks as somewhat different because it's only been in the past few years that blacks have been financially able to afford trips to other countries. this can be backed up by the number of passports issued to US blacks as compared to other colors and countries. i think they may not approach you at first but eventually they will.
bottom line: the name of the game is $RD !!!!
I am also a Black American and I have been referred to as gringo often ( I have also been referred to in different ways as well), which actually surprised me at first as I assumed a gringo was a White American. But as you say it is all good, as I notice that Dominicans often tend to refer to people by the color of their skin etc. (ie. Morena, Moreno, Rubia etc.), and they don't do it with the intention of anything derogatory.
Here are a couple of definitions along with the others that have been shared thus far:
n. Offensive Slang, pl., -gos.
Used as a disparaging term for a foreigner in Latin America, especially an American or English person.
[Spanish, foreign, foreign language, gibberish, probably alteration of griego, Greek, from Latin Graecus. See Greek.]
WORD HISTORY In Latin America the word gringo is an offensive term for a foreigner, particularly an American or English person. But the word existed in Spanish before this particular sense came into being. In fact, gringo may be an alteration of the word griego, the Spanish development of Latin Graecus, "Greek." Griego first meant "Greek, Grecian," as an adjective and "Greek, Greek language," as a noun. The saying "It's Greek to me" exists in Spanish, as it does in English, and helps us understand why griego came to mean "unintelligible language" and perhaps, by further extension of this idea, "stranger, that is, one who speaks a foreign language." The altered form gringo lost touch with Greek but has the senses "unintelligible language," "foreigner, especially an English person," and in Latin America, "North American or Britisher." Its first recorded English use (1849) is in John Woodhouse Audubon's Western Journal: "We were hooted and shouted at as we passed through, and called 'Gringoes.'"
then you also have this:
Gringo is a Spanish word used in Mexico and other parts of Latin America, generally to denote people from the United States. The term can be applied to any person who is known, or assumed to be from the United States regardless of race, or it can denote a strong association or assimilation into American society and culture. The term in its functional use is mostly encountered by Americans traveling abroad to Spanish speaking countries.[citation needed] The American Heritage Dictionary classifies gringo as "offensive slang," "usually disparaging," and "often disparaging."[1] Hispanophones disagree on whether the term is derogatory.[citation needed]
It kind of reminds me of the term, "Yankee", originally used by Southerners to refer to people from the north. To some it was a derogatory term, to others it was nothing more than for identification of where someone hailed from.