It varies depending on the size of the institution. Big places like Moneey Bay Aquarium and the Toledo Zoo usually have their own art departments. For those, I'd suggest doing a little research to figure out who's in charge of that dept. and sending them an inquiry letter and perhaps a few samples. Smaller zoos and aquariums are a lot more... well, I wouldn't say "laid back", but their departments are more flexible and open. I'd suggest talking to the education departments. They often need artwork for handouts, pamphlets, things like that. Be warned though-- since they're non-profit, they frequently can't pay a whole lot (especially in this economy). But it wouldn't hurt to give them a copy of your portfolio if they'e interested. Who knows-- they may have work for you in the future. I don't know if I'm just repeating stuff your professors already told you, but hopefully it'll help a little.
No this is all new to me, very useful! Our class barely touched on what exactly to do after graduating so I've been kind of building my portfolio without knowing where to go with it. Eventually I'd really like to illustrate science books but they don't really hire "new" illustrators for that, but maybe if I can get some work with a small zoo or aquarium to try to get some professional experience that would help.
Local science and nature centers are also a good place to look. For example, places in your neck of Michigan: the Moosewood Nature Center in Marquette and the Whitefish Point Bird Observatory in Paradise. Since they're also non-profit, they don't pay much (if anything), but they are good for establishing a base while you're just starting out. They can also sometimes provide contacts for more lucrative work.