The most essential day trip from Ruse is the Ivanovo Rock Monastery, 20 km south in the Rusenski Lom Nature Park. A local bus runs from the Ruse bus station to Ivanovo village; from there it's a 20-minute walk to the monastery. The gorge itself, carved by the Rusenski Lom river through limestone cliffs, is worth the journey even independently of the monastery.
Rusenski Lom Nature Park extends through a dramatic canyon system with more rock churches and medieval ruins accessible on foot from several villages. The abandoned village of Cherven, with its medieval fortress ruins, is about 30 km south and reachable by car or a combination of bus and walking.
Bucharest is 70 km north across the Danube and makes a viable day trip by road or train — bring your passport. The Friendship Bridge crossing can have queues; morning is generally faster than afternoon. Giurgiu, the Romanian city directly across the river, is a short hop rather than a destination, but the crossing itself is an experience.