All three schools are very different - size, location, campus life - but each of them is very reputable in their own right. Bowdoin may be ranked 6th but that’s in LAC ranking, Wake is 27th and UNC Chapel is 29th against the other National Universities … if rank is a factor they are all pretty even.
Think about where you see yourself being happy and fitting in the most, being involved on campus… think about your major and what opportunities each school offers for research/internship. Since they are all even academically speaking, I would be inclined to have my child choose the school that would cost less (sounds like Wake or UNC) because cost/lessening debt is big factor for us. Actually that is what we made D18 do, choose the most aid given/least cost option. An extra $20k isn’t too bad but an extra $80K a large amount of debt to carry in these uncertain times, especially if your major really warrants getting a Masters to be relevant.
If you really had your heart set on a smaller setting rather than a state uni go with Wake which is the middle of the road in size. Great school, larger than Bowdoin, still offers the sports watching fun of UNC, great traditions, fabulous campus, will be more diverse (not as many NC students as at UNC). The only thing it doesn’t give you is that OOS experience but you might be surprised if you were raised in NC that you will not like 6+months of winter… northern snow isn’t gone in a week - once it comes it’s your new landscape for months. Just some thoughts … good luck! You have great choices!