We're going to NYC in the last week of October.
Do I need to get tickets (for two people) ahead of time, or can we cue up on the day or evening we want to take the tour?
I would wait until a little later to book so you can be sure of the weather
A number of places that previously did not have timed ticket admissions have adopted them as a covid crowd control method - so check the sights on your wish list
As mentioned above, for a places like the https://www.esbnyc.com/ where the view is the primary attraction, it's usually better to wait until you have an idea what the weather forecast will be like
Also familiarize yourselves with the proof of vaccination & masking requirements for many indoor activities (dining, museums, theaters etc) https://www1.nyc.gov/site/doh/covid/covid-19-vaccines-keytonyc.page
When you say "Empire State Building Tour," do you mean that you want to go on a docent-led tour of the iconic building, or do you really just want to go up to an observation deck and look out over the NYC area?
If it's the latter, I would recommend going to Top of the Rock in Rockefeller Center or The Edge in Hudson Yards, instead. The views all around from those buildings are better than those from ESB. Their ticket prices are close to those for ESB's 86th floor observation deck alone and way cheaper than a ticket that also allows you to get up to ESB's 102nd floor. Wait times for tickets and elevators will likely be shorter, too.
From Top of the Rock, you get a direct view of the frequent evening light shows on the ESB facades -- you can't see them well while you're on the ESB observation decks -- you need to be a distance away from the building. At the Edge, the glass-floored deck protrudes from the building, and you will get dizzy looking down a thousand feet to the street
Check the ESB light show calendar:
Top of the Rock: