Šiauliai was the centre of Lithuanian bicycle manufacturing in the 20th century — the Vairas factory once produced more than a million bicycles a year — and the Bicycle Museum (Dviračių muziejus) tells the story across two floors. There are penny-farthings, Soviet-era roadsters, racing bikes ridden by Lithuanian Olympians, and a small workshop where wartime examples are restored.
The collection is far more interesting than it sounds, especially if you have any historical interest in transport. Allow an hour. The museum is on Vilniaus pedestrian street near the cathedral.