Update on getting to and from here by S-bahn train.
From the airport (terminal 1) to the hotel
Take S-bahn line numbers "S8" or "S9" from the airport terminal 1 train station and get off after 1 stop at "Frankfurt am Main - Gateway Gardens" station. Price is 2.10 euro each way. There is no train station at terminal 2, so you will have to use the free airport shuttle to transfer between terminals 1 and 2.
Once you arrive at the Gateway Gardens" station platform, you can either use the elevator in the center of the platform to exit or the escalators on either end. The escalator exit/entrance closest to the Hyatt Place is called "Jean-Gardner-Batten-strasse" and "De-Saint-Exupery-strasse. Once outside, the hotel will be on your right, next to a park like area.
From the hotel to the airport (terminal1):
Take S-bahn line numbers "S8" and "S9" from "Frankfurt am Main - Gateway Gardens" station to the airport terminal 1 in only 1 stop. Station is a 1 to 2 minute walk away from the hotel entrance. There is no train station at terminal 2, so you will have to use the free airport shuttle to transfer between terminal 1 and 2. Price 2.10 euro
Purchasing train tickets:
To buy the 2.10 euro tickets (price for one way in both directions) select "kurzstrecke" (short journey) on the machine.
The ticket machines at the airport and near the hotel all take coins or all major credit cards.
Avoid the rip off hotel shuttles all costs.
They only go to terminal 1, don't run all day, and are horribly overpriced.
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