Your attorney will have to file a request with the Court for permission to travel oversees. Whether you will be able to or not will depend on a number of factors: your past record, the nature of the underlying charge, the prosecutor's position, the reason for your travel, your contacts to the US etc.The main point is that it's entirely possible you will be able to travel
By "legal U.S. resident" do you mean "permanent resident alien," or are you a United States citizen?
If you are NOT a U.S. citizen, you can pretty much FORGET leaving this country while your DUI is pending. Most judges will be very leery of letting a non-citizen travel outside the U.S. while the person's case is still pending. As a matter of fact, if you DID, somehow, manage to leave the U.S. with a pending criminal case, you could be barred re-entry into the U.S. from your native country (or whichever country you were visiting).
If you are NOT a U.S. citizen, you need to consult with an experienced criminal defense attorney that also understands the immigration consequences of criminal convictions.
Please feel free to contact me through one of the web links below if I can be of further assistance to you or your family.
There should be no restrictions on your travel if you are not placed on probation as a result of the conviction. However, some countries, like Canada, have laws on their books that will prevent you from entering the country even with a Misdemeanor DUI conviction (assuming they find the conviction when you go through customs). To be extra safe, you should try to get your conviction "set aside" by the court once you have completed all sentencing requirements.
Silva Law Firm, PC. www.attorneysilva.com. This answer is based only on the information provided in the question and assumes the accuracy of that information. If the information is not accurate, this answer will not be accurate. This answer does not in any way form an attorney-client relationship, but is simply an opinion about the law and the facts that may be helpful to a person or the public at large.