I've seen a number of solutions on StackOverflow of this sort but I'm not sure what the best solution is to sort a categorical variable (default is alphabetical) based on a continuous variable.

Following is a simple example of this idea.

library(tidyverse)
data <- data.frame(Name = c('b','a','c'), Value = c(1,2,3))
g <- data %>%
ggplot(aes(Name, Value)) + geom_col()
g

The forcats package has the fct_reorder function. Not only will that work as a drop-in replacement for reorder in your case, it can also handle reordering based on each factor representing multiple rows. For example, that would allow sorting a boxplot by minimum, median, or maximum. There's also the fct_reorder2 function for 2d data, such as choosing colors of a scatterplot.

I'd like to plug the two posts linked from the forcats page -- they were very helpful for me in understands how strings and factors got to be so tied up and confusing in R, and helped me to understand the utility of correctly using factors in my visualization work:

and if you wanted your bars to be ordered with the highest on the left and the lowest on the right then you would change the arrange function to look like arrange(desc(Value))

If you don’t like nesting reorder in the ggplot call, you can just use it in mutate() without arrange(). I think it’s cleaner that way since it more closely captures the intent on a single line.