From my experience it's actually easier to do a "less touristy" trip in Hawaii than it is in some other places like the Caribbean. At least form the standpoint of local beaches being available and not just owned by big resorts. Main thing is that pre-planning is really important - go to actual travel forums on reddit or elsewhere and people can give you all the specifics of places to check out depending on time of year and island/area/cost.

There are also some common tourist type places that would actually be enjoyable because you can do them separate from big crowds. Like the Road to Hana on Maui - you can drive it yourself and there are plenty of quiet places to stop and take in beautiful sites like waterfalls, views of the ocean, etc.