時差ぼけ（じさぼけ）jet lag. Break down the kanji, and you get "time difference." I'm not sure about the ぼけ part.
隣り（となり）next to, next door, neighboring
住む（すむ）to live (at/in a place, house, city, country)
一家（いっか）a family, one family
弟一家 - the brother and his family
遊びに来る（あそびにくる）to come to play/hang out
- 遊ぶ does not mean literally "to play" in the context of two adult friends getting together. Then, it means to spend time pleasantly with.
食べに行く（たべにいく）to go to eat
- an elegant and effective way to join two actions together: ＿＿に行く or ＿＿に来る mean to go to __ or to come to ___. Use the -masu stem of the first verb; the -masu stem is the way the verb is conjugated for polite speech (遊ぶー＞遊びます) minus the ます.
Because I was jet-lagged, I slept until 9:30. My brother and his family, who live next door, came over, and we went to get lunch.