A rainy day in Jávea is the exception rather than the rule, especially in the tourist season: summer averages fewer than three rainy days, against just over ten in each of the other seasons. If it does turn wet, there are plenty of indoor options nearby.
The Museo Arqueológico y Etnográfico Soler Blasco, in the historic centre on Germans Segarra square, is a proper indoor museum with thirteen rooms of finds, ranging from the Neolithic to underwater archaeology. As in many Spanish town museums, the doors close for a break in the afternoon and it is shut altogether on Mondays, so check the current opening hours in advance on the Jávea town council website.
The Mercat Municipal, which you will come across again under shopping and markets, is also a genuinely covered building: a neo-Gothic market hall from 1946 with a saddle roof on pointed-arch tufa stone construction, built on the site of a demolished convent building. For an afternoon at the cinema there is Cine Jayan in the old centre, and a short drive away in Dénia are two free indoor museums: the Museo Etnológico, dedicated to the nineteenth-century raisin trade, and the Museo del Juguete, the toy museum in the old railway station.