Demonstrators smashed storefront windows and set rubbish and tyres alight in downtown Oakland, across the bay from San Francisco. A few miles away, students at the University of California at Berkeley protested on campus.
In Portland, Oregon, protesters blocked downtown traffic while chanting "not my president".
Hundreds of students in Pittsburgh, Pennsylvania, and Seattle, Washington, as well as in smaller towns around America, walked out of class in an effort to "stop president Trump".
Some 1500 high school students and teachers in Berkeley, California, walked out of classes chanting "not our president".
The students rallied in the courtyard of Berkeley High School, according to a school district spokesman, and marched toward the campus of the University of California at Berkeley, a city known for its progressive politics. Some teachers demonstrated with students.
"We're sitting here, setting our clocks back to 1950 electing this fool. You know? Trump honestly just makes us realise how much hate and ignorance is left," one female student told the rally, according to a live stream of the demonstration on the Periscope.
She said people of colour were afraid about the potential for discrimination, and immigrant families were now worried about the threat of deportation threatened by Trump.
Smaller groups of students walked out of classes in nearby Oakland and Seattle, while several hundred students at the University of Texas protested as well, according to local reports.
Anti-Trump rallies were planned in New York, Boston, Chicago and other cities, according to social media postings.
The demonstrations followed a night of protests around the San Francisco Bay Area and elsewhere in the country in response to Mr Trump's political upset.
Notable protests have also been held in Des Moines, Iowa and Austin, Texas.