1. Where do you live? I live in Sejong.
2. When is your summer vacation? My summer vacation at July 24th. = My summer vacation is on July 24th 
3. What do you do during your summer vacation? I watch movies.

NOTE:

1. "at" = is used for specific times (e.g., at 3 pm, at noon, at 10:15).  It is also used for holidays without "day" (e.g., at Christmas, at New Year)

2. "on" = Used for specific days and dates (e.g., on Monday, on July 10th, on Christmas day)