Is there an R package that easily identifies an observation that best "represents" the model?"

Hi, and welcome!

A reproducible example, called a reprex always helps clarify questions. I'll have to assume that you mean an ordinary least squares regression using lm(). A reprex would look like

fit <- lm(mpg ~ wt, data = mtcars)
abs_fit <- abs(fit$residuals)
#> Merc 450SL 
#>  0.0502472

Created on 2020-01-15 by the reprex package (v0.3.0)

This interprets the best fit as meaning has the smallest absolute residual, meaning lies closest to the trend line..