Population density really doesn't matter that much for a pandemic as infectious as COVID19. The number of people who live in the mountains or on a farm and only come into town every six months is very, very small.
The two big causes of massive early numbers of deaths, including in the northeast US (especially NYC, and NY state, NJ, and Philadelphia to a slightly lesser degree) and places like northern Italy, were
a) sending sick old people into old age homes. Other cities/states by and large did not do this. This drastically raised the average age of those who were infected in NYC, and caused the far higher death rates. 42% (!) of US deaths occurred in old age homes. Old age homes are pretty similar everywhere in terms of layout and design, regardless of local population density.
b) Assuming that ventilators should be used on every serious case, causing both damage from overoxygenation to healthy lung sacs and overdependence on mechanical respiration that doctors are having a tough time figuring out how to wean patients from. Those that warned three months ago (https://www.statnews.com/2020/04/08/doctors-say-ventilators-...) against ventilator overuse were completely vindicated in retrospect. This happened nationwide but most proportionately in NYC (in part because it was hit hard early so doctors were pioneers).
The big Western European countries hit hardest by the pandemic have 40-60 deaths per 10,000; the US is in the 30s, while states like Texas are in the single digits. NYC's death rate is 161 (!!); it singlehandedly prevented the US's death toll from being almost as low as Germany's. NYC's super-high death rate isn't replicated in the same way in other densely populated states that did not make the mistake of accidentally encouraging spreading of the disease among the elderly. Chicago, DC, and Boston were not hit anywhere as hard as NYC was.
Look, for example, at the NY Times dataset (https://www.nytimes.com/interactive/2020/us/coronavirus-us-c...). NYC's daily deaths peaked at about 10% of the cases, so we'll say 10% case fatality rate. Chicago's CFR is about 4%. Philadelphia's CFR is close to NYC, but Boston's is 6% and DC's is also about 4%. Basically, the NYC-Philly corridor handled this worse than anywhere else in the country.
Again, old age homes contributed 42% of COVID19 deaths, and largely due to big mistakes made in a portion of the northeast US. Those mistakes are no longer being made anywhere, nor is the "putting everyone on ventilators" mistake. This (plus the massive expansion in testing causing the average age of those testing positive to plummet) is why, although southern and western states' cases are rising (or in Los Angeles's case, never stopped rising from the start), deaths are not, and why national daily deaths continue to fall straight down from the mid-April peak.