Summer — June through August — is the obvious time to visit if you want the full seafront experience. The promenade comes alive, the Sea Life Centre fills up with families, the pubs spill onto the pavement, and the DART runs packed carriages of Dublin day-trippers on warm weekends. The beach itself is not particularly fine sand, but on a sunny Irish summer day people use it enthusiastically. July and August are the busiest months; if you want the seafront buzz without the crowds, early June or September is a better bet.
The cliff walk to Greystones is good year-round, but you need to dress for it outside summer. The path is exposed, the wind off the Irish Sea can be fierce in autumn and winter, and the Wicklow weather is changeable at any time of year. Waterproof layers are the standard advice and it is not wrong. On a clear winter day the views are extraordinary and you will have the path almost to yourself.
Killruddery House opens seasonally and is typically closed or on limited hours in winter — check before going if that is a priority. Otherwise Bray functions as a normal town year-round, and there is no bad time to walk the head.