I think it is relatively peak time for Kerala from October - March so everything would be expensive and not soothing. I think if you want to explore North,you can start with Nainital,Bhimtal,they are really beautiful. Apart from this,you can also try exploring Haridwar and Rishikesh,that would really pious place and mind refreshing.
A cyclon just left it's trail in Goa and even in Maharashtra the rains are pretty much continuous though the season is of winter. Am not 100% sure about Kerala but looking at the weather there I can be sure about one thing that visiting southern part right now is not that great of an idea especially costal region as either heavy rains or thunderstorms are expected almost everywhere. Hope it helped Happy Traveling!!