DailyHalacha.com quoting Rabbi Yitzchak Yosef says that one should attempt to avoid such a problem. However where that is the only option he should arrange prior to Shabbos that a non Jewish staff member will open his door when required. If one did not arrange this before Shabbos it is still permitted to ask a non Jewish staff member to open the door for him.
Rabbi Tzvi Goldberg from the StarK also permits this by leaving the key at the front desk prior to Shabbos.
Although electronic card keys may not be used and are muktza on
Shabbos, guests may leave them at the front desk before Shabbos, and
then on Shabbos ask non-Jewish staff members to open their door.
Rabbi Joshua Flug - end of page 22 quoting Minchas Yitzchak 3:23 and Yabia Omer Orach Chaim 7:36 says that since engaging an electric device that does not produce heat is only a Rabbinic violation in a case of need it is permitted. Due to the question whether this is truly a case of need when one knows in advance that a non Jew will be required to open the door for him, he brings two suggestions from Rabbi Yitzchak Zilberstein.
One is to leave some small gifts, chocolates, etc. in the room and when asking the non Jew to open the door say "I really want to give you a gift, however I can not give it to you as my room is locked", thus he is opening the door for his own benefit.
The second suggestion mentioned in the name of Rav Elyashiv Zatzal is telling the manager upon rental that he can only take the room if it is accessible over Shabbos and that he can not enter the room with a card. If the manager agrees to provide an arrangement where an employee will open it over Shabbos he is doing it for his own benefit.