The site of The Last Picture Show hasn't seen its final movie after all. The Royal Theater in Archer City, Tex. (pop. 1,800), symbolized the decline of small-town America in local hero Larry McMurtry's 1966 novel and Peter Bogdanovich's 1971 film. A sequel, Texasville, canonized the cinema in its current burned-out state. ''People come from all over the country to take pictures,'' says Abby Abernathy, who bought the theater in 1986 to save it from total demolition. Now Abernathy is behind a $2 million drive to construct a 20,000-square-foot performing-arts center behind a restored Royal facade. It's set to open in June 1998 for stage, music, and yes picture-show use. ''Our feasibility study said Archer City has eight avid theatergoers,'' laughs Abernathy, ''so obviously we've had to go outside'' for donations. The crucial supporter is McMurtry, who disapproved of previous proposals to rebuild the Royal as a memorabilia shop but thinks ''the notion of a living theater complex is far healthier.'' But won't a thriving Royal spoil the aura for decay-seeking tourists? ''Oh,'' says McMurtry, ''I don't think they're gonna miss the rubble.''