The basic meaning of 明 is bright (sun+moon). 明天 implies hope, a time that we look forward to. When the night is over, the bright sun rises and we can start fresh.
明年 “next year”, 明早 “tomorrow morning [formal, less common]” and 明朝 míngzhāo / mingjau [literary Chinese] are similar in that they can imply hope for a new beginning.
下個月 and 下個禮拜, 下星期一 etc (next week) have no such connotation of starting over bright and fresh. They are merely the next month/week in a sequence.
Other positive compounds with 明 include: 昌明 “prosperous”, 明君 “an enlightened ruler”, 賢明 “wise (ruler, policy), 開明 “open-minded”.
一綫光明 “A ray of hope”, (前途)光明 “a bright (future)”. One of China’s most important newspapers is the 光明日報 “Enlightenment Daily”.