Although a relative unknown in Hollywood circles, Uhry had begun to make a name in theatre circles. The Atlanta native met and formed a partnership with composer Robert Waldman when both were undergraduates at Brown. After graduating, both found employment with famed composer-lyricist Frank Loesser writing songs for TV and commercials. During the 1960s, Uhry and Waldman wrote the theme song for the TV series "Hootenanny", comedy song material for the series "That Was the Week That Was" and had a disastrous first run on Broadway with "Here's Where I Belong" (1968, with a book by Terrence McNally), a musical based on the John Steinbeck novel "East of Eden" that opened and closed in one night. To support his family, Uhry took a job teaching English at the Calhoun School, a private school on New York's West Side.
It was not until 1975 that Uhry and Waldman had another shot at Broadway with their adaptation of an Eudora Welty novella "The Robber Bridegroom". Produced under the auspices of John Houseman's The Acting Company, the musical featured Kevin Kline and Patti LuPone and earned Uhry a Tony nomination for his libretto. The show was revived the following season with Barry Bostwick in the lead and was modestly received. Uhry went on to provide the lyrics for the unsuccessful pre-Broadway tour of "Swing" (1980) and adapted George M. Cohan's "Little Johnny Jones" for a 1982 Broadway revival. With Waldman and book writer John Weidman, he collaborated on "America's Sweetheart" (1985), a musical about Al Capone that never made it to Broadway.
As a change of pace, Uhry turned to writing plays, not even informing his family about what he was working on. By day, he earned a living by teaching lyric writing at New York University. After Playwrights Horizons produced "Driving Miss Daisy", Hollywood beckoned. He was one of four writers who scripted the charming indie "Mystic Pizza" (1988), remembered more as being Julia Roberts' first major role. After the release of "Driving Miss Daisy" there was an aborted attempt to launch the premise as a TV series. Instead, Uhry became an in-demand screenwriter. His next produced effort was "Rich in Love" (1993), the story of a teen-age girl dealing with the divorce of her parents. He also worked on the script for Bruce Beresford's "Paradise Road" (1997), about European women interned by the Japanese during WWII.