In 1989 the French National Geographical Institute named a spot on the road to Moletai, 25km (15mi) north of Vilnius, as the centre of Europe. It's marked by a small, granite sculpture that has been vandalised, but a new sculpture - a pyramid with all the European capitals and their distances from the centre marked on it - is planned for the site. To get there, turn right off the Vilnius-Moletai road at the 'Europas Centras' sign.

Should you harbour an inexplicable urge to be the progenitor of generations of mutants, then a visit to the world's largest RMBK Chernobyl-style reactor plant may leave you with a warm inner (and outer) glow. The Visaginas town centre, 2km (1mi) west of the plant, features a Geiger counter that records daily radiation levels. The plant boasts two RMBK reactors, which are graphite cooled and have no containment system; if an accident occurs, radiation is immediately released into the open air. Visaginas is 120km (74mi) north-east of Vilnius. If you don't have private transport, trains connect Vilnius with the town of Ignalina, 50km (31mi) south of the plant, from where you can catch a local bus or taxi to Visaginas.

This old Lithuanian capital is now a small, quiet town in an attractive country area of lakes and islands. Most of the town stands on a peninsula dotted with old wooden cottages, many of them built by the Karaites - a Judaist sect originating in Baghdad that adheres to the Law of Moses. The Karaites were brought to Trakai by Vytautas the Great around 1400 AD to serve as bodyguards, and about 150 of them still live here. Their numbers are dwindling rapidly, giving legitimacy to fears that Lithuania's smallest ethnic minority could die out. There's a small Karaites museum here and an early-19th-century Karaites prayer house, both of which were renovated in 1997. Trakai is just 28km (17mi) west of Vilnius, connected to the capital by both train and bus.