If you're heading into eastern or central Slovakia by train, chances are you'll pass though Levice at some point or another. The city is a key transportation hub with lots of connections.
Levice is about 40 kilometres southeast of Nitra. Walking downtown from the bus and train stations will take you about 10 or 15 minutes. Along the way, you can detour through a substantial city park. The park looks a little run down, which makes it a surprise when you get to the main square and see some large hotels and city buildings with fancy baroque exteriors that wouldn't look out of place in old-town Bratislava.
The main attraction is the castle ruin not far from the town centre. It was built in the second half of the 13th century as a defence against the invading Turkish forces, and has been a ruin since 1709, when the troops of Hungarian rebel leader Ferenc Rákóczi burned it down and destroyed the castle walls on their way out of town. There are towering rocks included in the walls of the castle itself, making it an interesting place to walk around. There's also an amphitheatre inside the castle walls that was hosting plays in a town theatre festival when I was there. You can find out more about the castle (and pharmacy, unexpectedly) at the Tekov Museum inside the castle. There's also an art gallery onsite.
In fact, if the posters covering the town are anything to go by, it seems like there are a bunch of cultural activities going on in Levice – theatre, live music, and so forth.
Levice also has an observatory on Sokolovská Street – the third established in Slovakia – that offers workshops, as well as public observation periods on Friday and Saturday nights until midnight.