The centre is compact enough to tempt you into bad behaviour: Cathedral, tower, church, another church, photograph, next. Resist. Vilnius is a city of thresholds. A baroque street becomes a courtyard. A courtyard becomes a university passage. Cross one small river and a neighbourhood has declared itself a republic, complete with a constitution that takes absurdity more seriously than many governments take policy.
The useful thing to understand is that the layers are real. The historic centre is UNESCO-listed; Gothic, Renaissance, Classical and especially Baroque buildings sit inside the same walk. Užupis, just across the Vilnelė, symbolically declared independence on 1 April 1997. None of this requires a coach tour. Most of it requires shoes and enough time to turn down the street you had not planned.
Vytas: My favourite version of Vilnius begins when the itinerary develops a small administrative failure. You went out for one church and somehow acquired a courtyard, a coffee, a joke constitution and dinner. That is not poor planning. That is the city working correctly.