Two strategies that make the above into something more interpretable are taking the logarithm of the variable, or omitting the outliers. Both do not show the original distribution, however. Another way to go, is to create one bin for all the outlier values. This way we would see the original distribution where the density is the highest, while at the same time getting a feel for the number of outliers. A quick and dirty implementation of this would be
hist_data %>% mutate(x_new = ifelse(x > 10, 10, x)) %>% ggplot(aes(x_new)) + geom_histogram(binwidth = .1, col = "black", fill = "cornflowerblue")
Edwin then shows a nicer solution, so read the whole thing.