The most popular day trip is the Wagah border ceremony (covered separately on this site) — easy to arrange in the late afternoon.
Hiran Minar (Sheikhupura, 40 km north-west) is a 17th-century Mughal hunting complex built by Jahangir for his pet antelope Mansraj, who is buried beneath the octagonal minar. The surrounding tank and pavilion are pleasant and quiet.
Sheikhupura Fort, also Mughal, is in the same town and an easy combined visit.
Changa Manga, 70 km south, is one of the oldest planted forests in South Asia, established by the British in 1866. The forest has small lakes, a narrow-gauge railway loop, and is a popular weekend escape from Lahore — quieter on weekdays.
Harappa, 250 km south-west, is the ancient Indus Valley site — feasible as a long day trip but better as an overnight from Multan.