My favorite, hands down is MOBOT in St Louis. Mercer in Houston is another very nice and large one. There's a couple good ones in the Quad Cities area - Van der Meer in Davenport, Ia. and Quad Cities in Rock Island, Il. Texas also has a smaller botanical garden in Ft Worth, there's a pretty good sized one in Galveston. Ft Worth also as a downtown Water Garden that is a site to behold.
Though the focus is more on butterflies, 2 said Butterfly Houses have ton's of tropicals; they are The BF House in Chesterson, western suburb of St Louis (site is a subsidiary of MOBOT) and The Museum of Natural History in Houston.