The capital of the Budva Riviera is a safe resort, one of the best in Europe in this respect. Here you can walk the streets at any time of day or night, even away from the tourist trails.
If you follow the rule of "the statutes of other people's monasteries", there won't be any problems. Don't leave valuables in plain sight and don't provoke conflict situations. Montenegrins are tolerant of tourists' antics and try to treat problems with humor, but they won't let serious offenses go down.