Outside of Mexico, the Cinco de Mayo celebrations are generally an excuse to draw on fake moustaches and down tequila shots, and most foreigners have no idea what it's really about. The fiesta actually commemorates the defeat of the French army in 1862 in Puebla. Even though the superior French army went on to win the war, it lost the Battle of Puebla due to Mexican bravery and heroics. Nowhere else in the country is it celebrated with more gusto: with parades and night-long festivities. Puebla is THE place to be on Cinco de Mayo and it's essential to make reservations ahead of time.
The Festival Internacional de Puebla is usually in November and features concerts, exhibitions, street theatre and poetry readings. It makes the city buzz with an artistic vibe and is well worth a visit.
The weather is generally temperate with a summer rainy season from May until the beginning of October.