See if you can PL a hotel first for a very good rate. Use the infamous BFT or BB websites to see previous prices. I don't think spending HH points for the HHV for a less than 12 hour stay (assuming you leave at 7:30 a.m. for Lihue the next morning) is worth it. Plus, after rereading your post, I see you don't want to burn at the HHV. Sorry.

Why not try the Doubletree Alana Hotel (if you still want to burn HH points)? I have heard some good things about it and it's located relatively close to the HHV. However, staying in Waikiki means you'd either have to take a shuttle/taxi or rent a car, which might add more of a burden, both financially and emotionally, to your short layover. Of course, in the "Connecting in Hawai'i" thread, there's the Shower Tree option as well, which might be the most economical choice for a short stay on O'ahu (given its proximity to the airport and low rates). Any way you could get into HNL earlier or take a direct to LIH? That would be your best choice.

Alan does list some excellent suggestions, but further information is probably needed to narrow down your choices. Good luck on the HH -> SPG trade on the CC -- if I had enough *points, I'd trade you, but I've just started converting my stays from HH->SPG. It's a shame that HH also lacks a property on Kauai. IIRC, there was also an earlier post re: this question, which listed some excellent suggestions.

Edited to add: 11 days might be a bit long to stay on Kauai, although you can still make it an enjoyable vacation. However, IMHO an equal split of 5 days on Kauai and 5 on O'ahu would give you adequete time to explore both islands.

aloha