The weather in Istanbul is always untrustable. You sea a sunny sky and wear lightly and then you get cold in 1 hour or the opposite happens.
Istanbul is full of surprises and weather is one of them. Have a look at the forecast in the below link.
If it is rainy you museums is an universal option. Travelers generally prefer museums when it is rainy or when they have quarell with their partners:)
If it is sunny the best thing is walking and talking!