The surf tends to be a lot bigger in the winter. Oahu is bigger, population wise, which means more traffic, more people, and it can be a lot busier, so keep that in mind as well if you are looking for a relaxing vacation in Hawaii. When friends ask which island to go to I usually direct them to Maui, the Big Island, or Kauai. Outside of fishing I'm not sure what type of vacation you and your wife are looking for.
With that in mind I believe the bone fishing is the best on Oahu, not sure what it is like in Kauai, but believe there is some good bonefishing in Maui, or out of Maui to one of the nearby islands. There are some really big bonefish on the Big Island, but from my experience it is tough to fish for them with a fly, and I'm not sure if there are any guides on the Big Island. I had a few chase my fly when I was there last, but all of the bonefish I have caught where dunking squid in 30ft+ water as a kid.
Generally spring to fall is the best time to fish in Hawaii. Partially this is when there are calmer conditions and also some fish come inshore to spawn in the summer months. Other fish like trevally can be fun to target. If you can fit it in your suitcase I recommend bringing a stripping basket if you are doing the walk and wade thing. The lava can be a pain at times when trying to cast, even the small rocks in the sand, and choppy water or small surf can be annoying too.