I dived with Tulagi divers in 2004. It was the middle of the year, so I can't comment on the weather in Nov. In terms on diving, there will definately be enough to keep you occupied, especially if you are diving CCR. There are some big wrecks there, in particular the Aaron Ward that is in 70m and the Kanonwa (?spelling) that is in 50ish metres of water. There's also another wreck in the harbour right near the resort that is in 40m but is very affected by rain/run off unlike the other dives. We got on it and had about 2m of viz so called the dive, but on all the other dives had a min of 20m viz. The reefs there are also amazing and a favourite dive was Twin Tunnels - two lave tunnels that started at about 20m and went to 40m where you exit onto the wall. The wall continues down about another 30m and you get lots of pelagics in the area. In terms of non-diving stuff there is not really anything to do (no tv, no pool etc), so 10 - 12 days could wear a bit thin if you need some extra entertainment. We were there for 7 days and had a great time.
HTH,
Mel.b