Any one would not be bad. The character of the scenery is different in these regions, but there is plenty of it and all the activities mentioned in any of these areas. The Adirondacks tend more towards the mountainous side of things, so if hiking up (rather than hiking across) is more to your taste, that may be a better area.
Don't omit good insect repellent in any case.
I'm personally more familiar with New York than Michigan. Letchworth state park is one easy recommendation with fantastic scenery and a good bit of hiking and biking in the area, though it's arguably a bit west of the finger lakes region proper. There are many other fine options, too.
