4 days in Switzerland before a Rhine River cruise

Well, Golden Pass refers to a train route that goes from Montreux to Interlaken on a scenic mountain railway. It has nothing to do with a method of paying for train tickets. That would be the Swiss Travel Pass. Different kind of pass. One is low point in the mountains that train tracks follow and the other you show to the train conductor.

There is also something called a 30-day Half Fare Card costing 120 CHF. Then, every trip, whether on a train, boat, bus, tram, mountain cable car is half price. You need to have 240 CHF worth of full fare tickets to make it pay. People often buy the Swiss Travel Pass costing say 300 CHF, but end up only traveling for 200 CHF worth of tickets. They go home happy because it was easy and they had no idea they were over paying by 100 CHF.

So you have to price out where you are going and the cost of the tickets to make a business-like decision. You can do that at www.sbb.ch/en. But there is a trick (tricky Swiss), the first price you see assumes you have a Half Fare Card (I think everybody in Switzerland has one). You have to double that price to get what you actually would pay without one. You got to do your homework, Swiss trains are expensive.

You can buy these products at train stations when you arrive in Switzerland, like at Geneva Airport.

We opted for the half-fare card a few years ago when we spent 3-4 days in Switzerlanat the end of a mostly Italian vacation. We didn't purchase it until we entered Switzerland (I think Brig may nave been first stop on train from Milan). I think it was a wise choice. The savings on trams and especially the cable cars to mountain peaks alone were worth it. We stayed in Muerren (transfer from Interlaken), explored several sites in that area - both mountain peaks and valleys, and loved it! There are excellent maps online that show the routes available for using half-fare card, including some lake ferries etc.

Susan, Sam has summed it up well. The Golden Pass is a train route over a mountain pass, not a ticket pass (as is the Bernina Pass route). Switzerland has lots of mountain passes.
The ticket options are:
1) Pay full price
2) Buy a Half price Card for CHF 120 and pay half price for everything
3) Buy a Swiss Pass and only pay for trips up mountains
Examples from https://www.sbb.ch/en Geneva airport to Montreux, full fare: CHF 36.00, fare with Half Fare Card: CHF 18
Montreux to Lauterbrunnen (past Interlaken) full fare: CHF 82.60, with Half price card: CHF 41.30
Lauterbrunnen to Basel, full fare: CHF 68.60, with Half price card: CHF 34.30
For those three trips alone, a Half Price Card is not worth it, just pay full fare. But the choice depends on how many other side trips you are making.

So should I get tickets at the airport or purchase ahead of time here in the states?

The ticket prices do not have any discount for advance purchase. So just buy from the station on the day.

P.S.: A rail map showing all rail routes in Switzerland is here: https://www.sbb.ch/content/dam/infrastruktur/trafimage/karten/karte-sts-pass-gueltigkeit.pdf
All rail routes in Switzerland (all red lines on the map) have at least one train per hour, many have more. It is designed to be a "turn-up-and-go" service. No reservations and tickets are valid on any train on the day of purchase.