Planning to go to Solomon Islands for 10 days 22/12-01/01/19 (with some flexibility).

I do like diving and snorkeling (my girlfriend doesn’t dive tho). I like history. We can go of beaten track. We like ocean, boats, sailing.

Just wondering what are 2 or 3 top places we MUST visit given the time restrictions and our preferences?

Also, what is the best way to travel between the islands?

Many thanks,