I am traveling away from my home on Sunday morning for the duration of Pesach, and will be staying at a hotel.
Do I do a bedika at home on Motzi Shabbos and/or do I do a bedika in my hotel room on Erev Chag? Also, when do I say the beracha?
You have to do bedikah the night before you leave home. There is a dispute concerning the berachah, and it is best to say the berachah without shem and malchus.
At the hotel you have to do bedikah again on the night of erev Pesach (with a berachah).
I have seen some poskim write that in a “high quality hotel” which is always kept exceedingly clean, there would not be an obligation. However, it appears that even in such hotels there remains an obligation to search for chametz, because there are often alcoholic beverages left in the room that are chametz, or crackers and the like that must be cleared out.
See Kovetz Darchei Hora’ah Vol. 4 for a discussion of the issue; the Shevet Halevi 10:68 writes that there is a full obligation to check a hotel room, and one should check with a berachah.