Day trip in Moscow does not always mean "go in the morning, come back in the evening." Distances are vast, and the classic Russian approach is to board a train in the evening, sleep comfortably aboard, spend the day in a city some hundreds of kilometres away, and sleep one more night on the train home.
Vladimir is the easiest and most rewarding of the close trips — one of the oldest cities in Russia and a highlight of the Golden Ring, with white-stone cathedrals and the medieval Golden Gate. Buses from the square in front of Kursk Railway Station (Kurskaya metro) run every half hour and take about 2.5 hours; ask to be let off at the Golden Gate rather than continuing to the bus station.
Vologda, about 500 km to the north, rewards the overnight-train traveller with its extraordinary carved wooden houses and golden domes. The best time to go is June or July, when the white nights keep the town glowing late, or deep winter for a real "Russian winter." Train #234 Moscow–Arkhangelsk (via Vologda) is the practical choice, though it does not run every day, so check the timetable.
Kazan, the Tatar capital on the Volga, is a longer haul — two nights aboard a train — but doable for the determined. Trains leave from Kazansky Vokzal (Kazan Railway Station); the daily #002 Moscow–Kazan departs around 19:20 and arrives 07:25 the next morning.
Closer to the city, two destinations make genuine single-day outings without an overnight train: the aristocratic estate of Arkhangelskoye, 20 km west with its Yusupov Palace and Italian gardens, and the Borodino Battlefield, 120 km west, where Napoleon met Kutuzov in 1812 and where the world's oldest battlefield museum still stands.
