Fig.: to party and celebrate with enthusiasm in bars and restaurants

After living in a farm in the country for 34 years, it's high time I kick up my heels and paint the town red. New York, here I am!

Dopo aver vissuto per 34 anni in campagna in una fattoria, ho deciso che è arrivato il momento di spassarmela e darmi alla pazza gioia. New York, arrivo!

On the first night ashore after a non-stop three-month sailing, the sailors painted the town red

La prima sera a terra dopo una navigazione ininterrotta di tre mesi, i marinai si sono dati alla pazza gioia

After the final exam in college, all the course students went out together to paint the town red

Dopo l'esame finale, tutti gli studenti del corso sono usciti insieme a festeggiare e fare bisboccia

The origin of this phrase is disputed. According to one theory, it originated with the Roman Empire. Roman soldiers used to wash the walls of a newly conquered town or city with the blood of the vanquished. This was usually accomplished with pleasure, so the term came to be applied to a great night on the town.
Others link the color red with the color of the pioneers' villages set on fire by American Indians. Another explanation alludes to a town's red-light district with its brothels and saloons; not to mention the theory that associates the color red with violence, by which the meaning of our idiomatic phrase would be “to do violence in town”