It would generally be illegal for a court to impose terms preventing you from leaving the state or country while on summary probation [which most misdemeanor DUIs are, but not all!], but there are some courts which have started imposing those illegal terms over the past couple of years, so you need to check your terms before you head out, and if there is such a term, you need to litigate it and have it stricken.

Mr. Davis is correct. It depends on the terms of your probation. Froim your description, it sounds like you took a standard plea to a 1st or 2d DUI conviction. If so, you're probably on unsupervised probation which should not preclude your leaving the county. However, only you and your attorney know for sure. Also, each county has different rules about the terms of probation offered. You should consult the attorney who represented you in your case.

The answer depends on the terms of the probation, and you should check, but, generally, at least in California, a misdemeanor DUI conviction will have what they refer to as Summary Probation. That should not affect your ability to leave. Be aware though, some countries will restrict access to people with a DUI conviction. Best to check that before leaving too. Good luck.