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I've read reports about how thousands of localities in the US have severe lead contamination of their tap water (and lead is a very dangerous substance to imbibe at any concentration). On the other hand, answers here on the site, e.g. the accepted answer to:

Is tap water in US safe to drink?

claim that

Virtually all municipal water systems in the United States provide clean and safe drinking water.

So, which is it? And more importantly - how can I tell whether tap water where I'm staying in the US is really safe to drink?

The report you cite does not contradict the answer you cite. The report did not as you claim find "thousands of localities" with "severe lead contamination of their tap water." Rather, the report concerns blood lead levels in children, which can be, and often are, elevated by causes other than lead in municipal water:

Reuters conducted a nationwide analysis of childhood blood lead testing data at the neighborhood level.

The report only uses the word "water" in describing the situation in Flint and in discussing Milwaukee:

The city still has 135,000 prewar dwellings with lead paint, and 70,000 with lead water service lines. Most of its poisoning occurs in a few zip codes, where Baker says $50 million has been spent to protect children.

By contrast, discusses lead paint at some length. A sampling:

• In explanation, she pointed to the peeling paint on her old house. Kadin, she said, has been diagnosed with lead poisoning.


• Like Flint, many of these localities are plagued by legacy lead: crumbling paint, plumbing, or industrial waste left behind.


• Since the heavy metal was phased out from paint and gasoline in the late 1970s, children’s average blood lead levels have dropped by more than 90 percent. That success story masks a sober reality in neighborhoods where risk abatement has failed.


• St. Joseph, Missouri, is filled with old homes that for a century featured lead paint and plumbing. From 2010 to 2015, more than 15 percent of children tested in seven census tracts here had elevated lead levels – well beyond the Missouri average of 5 percent.


• McCush, a certified lead inspector, says his office told one family that sanding paint off their walls was poisoning their son. “The dad said we were full of baloney,” he said. “He wasn’t going to stop working.”


• At son Kadin’s one-year doctor visit, Mignery was told his lead levels were so high that, without quick intervention, he would need to be hospitalized. An inspector visited the home and found the culprit: old peeling lead paint. The family could only afford a partial fix. “It wasn’t easy having to repaint all the rooms downstairs,” she said. “We want to do the outside here, too.”


• Across the street is the old rental house where, as a baby, Brandon was exposed to peeling lead paint.


• A mile away, in Milwaukee’s census tract 88, Isaiah Martin, 18 months old, recently ingested old paint in a family home and on the porch outside


• In the 1990s, starting at age 2, Gray lived in a row house in Baltimore’s Sandtown-Winchester area tainted with old lead paint, ...


• Edward Brown Jr., 2, was first tested last year. He’d been living with his mother, Victoria Marshall, in a central South Bend home. An inspector found lead paint inside and contaminated soil outside.

Finally, the answer you cite recognizes the circumstances reported by Reuters:

Some old buildings may have old pipes that can impart an off taste or even leach lead into the water. While it may be worth testing for lead someplace where small children will be living for years, I wouldn't be concerned about an adult taking a five week course. You should also avoid eating peeling paint.