The Amtrak station in PS is far outside town, there is usually no taxi service on site, and the scheduled arrivals from the east are normally late at night, if they are on time. I like train travel, but it is not a good choice for PS, unless you have a friend with a car in North Palm Springs, who is willing to pick you up at any hour. There are air connections from the cities you mention, but few international visitors arrive at those cities.