If you consider Budapest weather, the best time to visit can be spring, late March trough May or fall, September through the end of October. However, what is good about Budapest is that travel to the city can occur at any time of the year, with events going on throughout the seasons and the temperature being relatively moderate in comparison with many locations.
Good news: all in all there’s not really a bad time to visit Budapest!
For frame of reference for American visitors, the climate is similar to that of Pennsylvania, with the typical four seasons changing gradually into one another with few sudden changes or long-term temperature extreme. However, you must note that weather in Europe is very unpredictable from year to year. What’s sure that in spring and summer the amount of daylight is much more than in late autumn and winter.
Budapest weather in four seasons:
Winters are usually cold, especially in January, with some swony spells between December and February. Temperature averages around 30-40°F/-1 +5 °C In January and February it can be very cold at night.
Spring brings abundant sunshine and not too much rain.
Temperature averages around  45°F/6°C in March to 61°F/16°C in May. From April to May during the day the temperature is usually pleasant for walks, in the evening it gets cooler.
In summer Budapest has as much sunshine as many Mediterranean resorts. Summers can be very hot, especially in July and August, average 70°F/21°C, with some extremely hot days/weeks even around 100°F/38°C at midday.
Air conditioning in 4-5 star-hotels is guaranteed but if you book a cheaper hotel or apartement you should make sure they have airconditioning.
Falls start also mild. In September it can be quite warm and even in October you can expect some nice sunny days, although daylight is significantly less and it gets dark much earlier than in summer.  Evenings are chilly. November can be quite rainy and it brings a drastic fall in temperature.
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