Southern Sudovia is part of Poland politically but an extension of Lithuania culturally/historically. This area changed hands many times but remained in Poland after the 1920 war. Locals, however, put a great emphasis on their Lithuanian ethnicity.
A good example of that is a Prussian-Yotvingian settlement near Punsk - an atmospheric reimagination of how a prehistoric pagan Baltic village may have looked like. Constructed entirely by a single Lithuanian enthusiast over many years it has a single over-arching style which makes it even more believable (even if perhaps less authentic) than reconstructions by historians.
The "settlement" includes a small castle, watchtowers, totems, meeting circles, sacred fires, runic inscriptions, a bridge, an archery range, political-philosophical inscriptions on behalf of the extinct Prussian and Yotvingian tribes to which the owner self-identifies. Everything is built of wood while decorations are of stone and bones. The forest is both around the settlement and inside it; nearly no modern buildings are visible from anywhere. The area is no museum, however; everything may be touched and there are well-integrated benches, WCs. Lithuanian neo-pagans even hold their celebrations there.
Punsk village (pop. ~1200, 80% Lithuanians) also has two Lithuanians-related museums and one skansen. A multitude of Lithuanian symbols on the area's walls and fences are another proof of the local feelings.
Sejny (Lithuanian: Seinai) town 23 km south of Punsk has a castle-like 19th-century former Lithuanian priest seminary, while Wigry (Lithuanian: Vygriai) hosts a massive 17th-18th centuries monastery.
The main sights of Poland (Warsaw, Cracow, Torun, Gdansk) are all far away (300-800 km) and the local roads are no highways, making it impractical to combine a visit there with a Lithuanian voyage unless you plan a larger Baltic trip. The Poland's closest prime touristic place to Lithuania is the former Adolf Hitler's bunker some 170 km away.