"Eastern Europe" as a category is misleading. The countries inside it have less in common with each other than first-timers expect. Czechia is industrial-Habsburg-cool. Romania is Latin-mountain. Hungary is its own thing. The Baltics are nordic-influenced. The Balkans are something else entirely.
This guide is per-country: which city to base, which second city is worth a side trip, the most common mistake travelers make.
Czechia
Base city: Prague. Stay in Vinohrady rather than the Old Town. Same train access, dramatically cheaper, far less stag-do noise.
Second city: Brno. Smaller, modernist architecture, fraction of Prague prices.
Common mistake: Booking inside Old Town Square. The acoustics, prices, and bachelor-party density punish you.
Hungary
Base city: Budapest. District V for first-timers, District VII for ruin-bar nightlife, District VI for the Andrássy Avenue middle ground.
Second city: Debrecen or Pécs, but realistically Budapest is most of the Hungary trip.
Common mistake: Booking on the Buda side for a short trip. Buda is for honeymoons and quiet stays; the action is on the Pest side.
Poland
Base city: Krakow. Kazimierz is the local-life answer; Stare Miasto is the postcard answer.
Second city: Gdańsk. Architecturally distinct from Krakow — Hanseatic, on the Baltic — and 3 hours by train.
Common mistake: Treating Warsaw as the natural "capital tour" answer. Warsaw is fine but Krakow is more rewarding for short trips.
Romania
Base city: Brașov. The Saxon old town inside the medieval walls is beautiful and walkable; Piața Sfatului is the obvious base.
Second city: Sibiu. Smaller, more atmospheric, the Saxon "eyes-of-Sibiu" rooftops.
Common mistake: Bucharest-only itineraries. Bucharest is rough and rewarding in equal measure, but Transylvania is most of why people go to Romania.
The Baltics
Tallinn: Stay in the Old Town (Vanalinn) for one night, then Telliskivi if you want the creative quarter. The Old Town is heavily tourist-managed in summer.
Riga: Old Town is the obvious base. Skip if you've done Tallinn and Vilnius.
Vilnius: The Old Town is large, atmospheric, and the underrated entry of the three.
Common mistake: Trying to see all three in 5 days. Pick one, possibly two with the bus between them.
The Balkans
Bosnia & Herzegovina: Sarajevo's Baščaršija for the Ottoman-era atmosphere, Mostar's Stari Grad for one night by the bridge.
Croatia: Already covered extensively elsewhere. Don't sleep inside Diocletian's Palace in Split (loud); don't sleep inside Dubrovnik's walls (overpriced).
Slovenia: Ljubljana, then either Bled or Piran depending on whether you prefer mountains or sea.
Montenegro/Albania/North Macedonia: Worth their own dedicated guides. Generally: stay where the mid-priced car-rental is (Localrent has strong coverage in all three) because public transit between sights is thin.
Bulgaria
Base city: Sofia is fine; Plovdiv is more rewarding. Most weekend trips work better with Plovdiv as the base and a Sofia day-trip than the reverse.
The cross-cutting advice
Eastern European cities reward staying just outside the most-recommended neighborhood. The price gap is bigger than in Western Europe, the walkability gap is smaller. Vinohrady not Old Town, Kazimierz not Stare Miasto, Beyoğlu not Sultanahmet. The rule has held for a decade and isn't changing.