The two most popular day trips from Varadero are Havana (140 km west) and Trinidad (around 350 km). Havana is easily done in a day by bus or organized tour — you won't see everything but the old city, the Malecón, and a rum bar make a satisfying excursion. Trinidad is a longer journey and better done as an overnight.
The Bellamar Caves near Matanzas (40 km) are a closer option — Cuba's most accessible cave system and a reasonable half-day trip. Zapata National Park to the south is Cuba's largest wetland reserve, good for birdwatching and crocodile sightings.