As with all European capitals the best time to visit Bucharest is during spring or autumn- April, May, September. During summer the weather is too hot (e.g. up 40 degrees Celsius in sunlight).

Summer and winter are the good sesons for visiting the Prahova Valley. Also during summer you can go at the seaside or visit the nice Danube Delta. 

Spring is pleasant with cool mornings and nights and warm days.
Summer is quite warm, with extended sunny days. The hottest areas in summer are the lowlands in southern and eastern Romania where 100 F is often reached in July and August. Temperatures are always cooler in the mountains.
Autumn is dry and cool, with fields and trees producing colorful foliage, much like New England.
Winters can be cold, especially in the mountains. While not the rule, abundant snowfalls may occur throughout the country, from December to mid-March.

There are significant regional differences of the climate between different regions of Romania.

Warmest month: July
Coldest month: January