Vila Velha has a tropical climate with warm weather year-round. The hottest months are December through February, when temperatures regularly exceed 30°C and humidity is high. Rainfall peaks in these months as well, with afternoon thunderstorms common but usually brief. If you want beach weather without overwhelming heat, March through May is a good window.
The winter months of June through August are mild and drier — temperatures drop to around 20–25°C, which is comfortable for sightseeing and walking. These months also see lower tourist numbers and cheaper accommodation.
The most important festival is the Festa do Espírito Santo, held over a week in May (the exact dates change with the liturgical calendar). It's the largest religious festival in the state and one of the biggest in Brazil, centred on the Convento da Penha. The city fills up and the pilgrimage creates a remarkable atmosphere — worth timing a visit around if you can.