Miskolc is at its best from May to September, when the Bükk forests are full and the Lillafüred area is green and accessible. Summer can be warm in the valley (the city traps heat on hot days), which makes the cave bath at Miskolctapolca particularly appealing — the water stays 30°C regardless of the weather outside.
The Opera Festival usually runs in late June, bringing international opera companies to the city for a week of performances. If you are planning a visit and enjoy opera, it is worth timing around.
Autumn is good for hiking in the Bükk, with beech forests turning gold in October. Winter is cold and the mountains can have snow, which suits the forest railway and cave visits but limits the outdoor appeal.