Will (aka Short_leaf) asked about arboreta/plant places in the midwest, over on the trees forum. This seems the place for this kind of expanded travel commentary.

The mid Midwest (central MO and westward) is an area of the US I don't know well, but I'm not afraid to offer an opinion where I have been. One of these days, I'll get out there. But since Will asked about arboretum experiences...

As a generality, any institution that maintains a grounds of any size (multiple acres usually; sometimes tiny properties can have treasures, too) will have collections of plants worth seeing. The labeled places suit most that haven't sharpened their ID skills yet, so arboretums, botanic gardens, and the like get the most press/visits. Included in a traveler's itinerary ought to be places like cemeteries/churches; college/school campuses; major corporate campuses; sculpture gardens/collections; parks and town squares; big nurseries/garden centers; and grand estates, hopefully now publicly accessible.

Having some good references on plants will yield more suggestions on "where to see this" or that than any human could possibly visit, but will sure make you try. Will asked in another thread about good books on seed propagation; one of the best books on locations of fine tree individuals is by the same author, Michael Dirr, specifically for east of the Rockies (mostly east of the Mississippi River, his area of expertise). But there are many more. RonB posts often, and his favorite author is Arthur Jacobson (sp?) who lists big trees of many types in his text on North American landscape trees.

You might be able to tell that my interest trends towards woody plants. Not to worry; all these types of sites are generally replete with all the strata of plant life, and occasionally you'll be pleasantly surprised by what you find when you've gone looking for something else.

Surprises often include learning the sense of place: culture, history, people, etc. IN ADDITION to the wonder and beauty of the plants. Education just kind of sneaks up on you.

Check GW's directory of gardens/arboreta. As a first cut, to keep this post digestible, here are some places I'd look to see in the MO-IL-IN areas (and not repeating what Rue_Anemone linked to for IN):

University of MO-Columbia (Mark Coggeshall, plant propagator extraordinaire ought to be your contact)

Missouri Botanical Garden, and its satellite Shaw Arboretum

Forest Park, St. Louis and its many parts

Gateway Arch and grounds

L____meier Sculptural Park, St. Louis (sorry don't remember exact spelling right now)

Southern IL University, Carbondale IL

Starhill Forest/Arboretum, Petersburg IL (oaks, oaks, oaks)

John Deere HQ, Moline IL

Sears HQ, NW Chicago suburbs

McDonalds HQ, NW Chicago suburbs

Chicago Botanic Garden and Morton Arboretum, Chicago area

Grant Park and Columbus Park, Chicago

University of IL, Champaign-Urbana IL

IL State U, Bloomington-Normal IL

Indiana University, Bloomington IN

Mill Valley Park, Columbus IN

The city of Columbus IN, including Cummins Engine offices

Hidden Hill, Utica IN

Obviously, this is a never-ending proposition. Probably a post per state is a better way to go. Additions welcomed.