While I don't think Hawaii ever has a true "low" season, my wife and I take all of our trips there during May-Sept so that we can use points and miles for the trips. We've done 4 weeks in hotels using MR and HH awards, and have redeemed UA and AA miles to get there. We were able to pick & choose our dates for the most part - we usually book in January.

Added bonus: none of our hotels were terribly full, so we received great rooms on all of our award stays (not suites, but high-floor full-ocean-view rooms). Also, booking activities and tours was fairly easy to do at that time of year - we didn't need to prebook luaus, boat rides, or tee times weeks in advance. Just make phone calls a day or two beforehand to arrange the activities...

As for Western Europe, I think the airlines consider May 15 - Oct 15 as the high season. The big hotel chains are probably similar... However, I have spent time all over Europe in September and loved it: I didn't feel that September was a bad month to be there at all. (I get the sense that max-peak tourist season is more like July-August.)