For the most part, you will be able to travel outside the United States after a conviction for most misdemeanors and violations (including DWI and DWAI). There are, however, some exceptions.

Travel to Canada, South Africa, China, Japan, Australia, and New Zealand will be difficult. Those countries all have strict rules about denying entry to people with DWI or DWAI convictions on their record. Mexico has rules on the books saying that you could be denied entry, but in practice I have never heard from a client or read about a person who was denied entry into Mexico.