Not quite a reprex but good enough I think.
To plot dates in the x-axis you need to use a proper date variable, not character strings, and to customize the "date breaks" of your plot you can use the scale_x_date() function. Check this example:
library(tidyverse)
d.wastewaternew <- data.frame(
stringsAsFactors = FALSE,
ï..DateResult = c("9/1/2020","9/4/2020",
"9/10/2020","9/15/2020","9/17/2020","9/22/2020"),
Hall = c("Booth Hall","Booth Hall",
"Booth Hall","Booth Hall","Booth Hall","Booth Hall"),
SARS2_levels = c(0, 0, 0, 0, 0, 0),
sampledate = as.Date(c("2020-09-01","2020-09-04",
"2020-09-10","2020-09-15","2020-09-17","2020-09-22"))
)
d.wastewaternew %>%
ggplot(aes(x = sampledate, y = SARS2_levels, color = Hall)) +
geom_line() +
scale_x_date(date_breaks = "1 day",
labels = scales::label_date_short())

Created on 2021-04-18 by the reprex package (v2.0.0)