Look further into the transportation situation before choosing Whidbey. Buses are free but limited in where they go and how often/how late, and they don't run on weekends. Island Transit is the name to Google for that. There is no Uber/Lyft on Whidbey. Taxis are extremely limited as well, south of Oak Harbor it's I think just one company with only a couple cars/drivers so it can be a long wait and costly (though not always... Plan ahead, call them and make reservations). Depending on where you want to go and when, it could be awesome, but without a car I'd definitely check those details first. I don't know at all how this compares to Bainbridge.

Also Whidbey has tons of forested areas especially on the south end. South Whidbey State Park, Trillium forest, and Saratoga Woods are all forested and awesome trails to check out. Greenbank Farm also has a portion of trails that go through the forest (and great views from the non-forested off-leash dog area. And of course like another commenter said, Fort Ebey, Fort Casey, and Deception Pass are all worth visiting.

Edit: Island Transit does have some routes on Saturdays, none on Sundays.