David Letterman will bow on Broadway Aug. 23, the web said. But first the Ed Sullivan Theater, the new home for his upcoming CBS series, will get a total renovation.Ed Grebow, CBS’s senior VP of operations and administration, said yesterday the network is going “to restore this theater to its past glory.” CBS and renovation consultants have six months. According to Grebow, the network started looking for facilities back in November. The web, Letterman and show executives visited 15 Broadway theaters and CBS’ Los Angeles facilities before coming to a decision. The executives decided three weeks ago that the show would stay in N.Y. and about 14 days ago settled on the Sullivan Theater. CBS has called on architect James Stewart Polshek to oversee the $ 10 million in renovations to the theater and adjacent 13-floor office building. The theater must be rewired, air-conditioning ductwork must be installed to keep the room at Letterman’s requested 62 degrees, and a control room must be built.