Combating drugs, crime and AIDS, providing affordable housing and improving public transportation systems are the most pressing issues facing this country's mayors, says Tom Cochran, executive director of the U.S. Conference of Mayors.

"This is one of our most significant meetings in the history of the conference. We will remember Salt Lake City for what was decided here," Cochran said. "The question is: How will cities fare in the post-Reagan era?"The 56th annual U.S. Conference of Mayors began Friday in Salt Lake City, and will continue through Wednesday. Eight hundred mayors and city staff members are attending.

Cochran said the national organization represents an urban force with a power that presidential candidates have to listen to. "We believe that the person that wins the presidency will have to talk our issues."

Democratic Presidential Candidate Michael Dukakis will woo urban support by speaking to the mayors Sunday. Conference organizers are still hoping that Dukakis' Democratic challenger, Jesse Jackson, will make the Utah trip, as well as Vice-President George Bush.

"The question is: `Where is Vice President George Bush?' We are very concerned that he come to us and talk to us at this time," Cochran said.

But organizers won't write off Bush until the conference winds down Wednesday.

Jackson and Dukakis were among the seven presidential hopefuls that addressed mayors at last year's conference in Nashville, and Jackson was the only candidate to speak to the group in 1984.

Mike Brown, public affairs director for the conference, said the organization has already had a powerful impact on this year's presidential campaign, and that impact will continue as mayors are involved in planning presidential candidates campaign platforms.

"We're asking the candidates to give us their vision of the cities. We're asking them, of course, to include the mayors in the planning for their administration," Brown said.

"Four years ago, during the campaigns, the word cities was not used by either the Republican or Democratic candidates. The mayors were not very happy with that. They were determined that that would not happen again in 1988. And it hasn't."

Conference sessions are planned to provide networking opportunities for mayors as well to forge a united urban lobbying force.