I stayed in Kaui a number of years ago in Lihue which is half way between the north and south on the east. It was kind of a compromise. We knew we would be driving both north and south and thus never had as far to go.
For some reason the first day you get to Kaui, you want to go drive and look around the island. Anyway, January is considered the rainy season. That's when I went. Summer should help out in that regard. That said, Hanalei is beautiful, it's worth seeing, but being there on a cloudy day is not as fun. You'd think it wouldn't matter but it's just so much better being at the beach when it is sunny.
I think I would stay south, if you can find a nice place you can afford. Staying in a cheap yucky place is no fun, even if sunnier.
The Hyatt in poipu which is south is nice but pricy. There is a great restaurant nearby called Roy's with fantastic pacific rim cuisine. Also a fun casual open air restaurant right on poipu beach, although the name escapes me. If you could find a website with more weather info on kaui, that could help.
Snorkeling is fun at poipu beach, by the way. I'm sure whichever you choose will be great. The both have their upsides.
Here is a tip on selection of hotels, whether in Hawaii or not. I'd pick the cheapest room in a ritzy hotel over the priciest room in a cheap hotel any day. In other words, a room without an ocean view at the hyatt beats a room with an ocean view at a less luxurious hotel any day. You can always go outside and see the ocean, but its so nice to have a beautiful room, tastefully decorated etc, versus a dated room with a view. Watch out too, cause it seems like all hotels show pictures of the hotel and rooms when they first opened, so the fact that it might be dated looking now won't be apparent.