The Cheltenham Festival in March is the reason many people visit — four days of National Hunt racing that transforms the town. Book accommodation at least six months ahead if you want to attend; prices triple and the town is genuinely very busy.
The Literature Festival in October is the other major event, drawing authors and audiences for ten days of talks, readings, and debates. The Jazz Festival in April is smaller but well-curated.
Summer is the obvious time for general sightseeing — the Pittville Park and gardens are at their best, and the lido is open. The town is pleasant year-round given its indoor attractions, but winters can be grey and quiet outside the Christmas market period.