Dylan, when I view my trips I can view a receipt that does separate the cost into service fees and nightly rate. The nightly rate includes taxes though. You just have to view the detailed receipt.
If that is not enough for you, and you need to know exactly how much was taxes, I know as a host I can see the amount of taxes that were collected. (I live in a state where taxes are collected by Airbnb). If that is the case you could contact your host and see if they could tell you how much of the fee was for taxes. Another way to do that is to go to the same listing you stayed at, and enter two upcoming dates. See if the price is the same as what you were charged initially - if Airbnb collects taxes in that state, an itemized amount will pop up and you will be able to see automatically what the tax rate is.
It is also possible that you rented from someone in a state that lacks a tax agreement with Airbnb. If that is the case, Airbnb wouldn't know the taxes that were collected, and the host may or may not be collecting and tracking taxes. In those states, since Airbnb generates your receipt, they only know the total charge the host charged you, and the Airbnb service fee.