How can I determine whether or not an airport has an ATIS?
The frequency for and class of the ATIS is on the VFR Sectional Chart right where you have indicated. It will also be listed in the US Chart Supplement under Weather Data Sources. The ATIS Code will never be listed as it is a function of the ATIS itself. And, it changes over time.
The left side of that section of your VFR Navigation Log is meant to be filled out shortly before takeoff. The right side of that section of your VFR Navigation Log is meant to be filled out shortly before arrival. It is helpful to have the information beforehand in your preflight planning in order to make a go/no-go decision. But, it’s primary purpose is to inform the pilot of current takeoff conditions at the time of departure and arrival. At a controlled airfield, you will be required to confirm you have the most current ATIS information by relaying the ATIS Code to ATC. That ATIS code is acquired either by listening to the ATIS over the ATIS frequency, over your cell phone at the phone number given in the US Chart Supplement, or electronically. The ATIS Code changes each time the information on the ATIS is updated. For a Class D, E, or G airport, in most cases, that is once every hour around the 45-55 minute mark. It can be more frequent for a more advanced, automated digital, non-automated, or human recorded ATIS at a Class B, C or large D airfield.
By the way, many air traffic controllers I have talked to have said that they must hear the ATIS Code either at the beginning, right after your tail number, or at the end, as the last piece of information of your initial transmission/radio call. But, I do not have any citations or references for this. Maybe another poster can provide one.