A year before New York's Senate election, the television advertising battle for the hearts and minds of upstate New York voters has begun. State Democratic leaders yesterday unveiled an ad to begin airing today that touts first lady Hillary Rodham Clinton and the "conversation" she has started in New York about the issues "closest to our hearts."

The 30-second spot will run for about a week in Buffalo, Rochester, Syracuse and Albany. Clinton's likely Republican opponent, New York City Mayor Rudolph W. Giuliani, began airing an ad of his own in the same cities last week. Giuliani's ad touts his accomplishments in New York City and ends with the line: "Rudy, ready to do even more, for all of us." Neither of the ads explicitly mentions the Senate race.

That both campaigns are focusing on upstate New York reflects just how competitive the region is.

The Clinton ad, which also will run in several other cities upstate, picks up the themes of the "listening tour" that Clinton conducted last summer and that have emerged as her campaign issues: families, education, health care, jobs.

The ad's images are of a farm, a main street, a lemonade stand and smiling children, of course with Clinton in there talking and listening to people and being cheered by an approving crowd. Says the announcer: "It's about leadership that's on our side. Call Hillary. Tell her to keep fighting for children, for families, for our future." The ad invites callers to the state Democratic Party.

Giuliani's ads are being paid for by his campaign committee, but the ad boosting Hillary Clinton is being financed by the Democratic National Committee and New York's State Democratic Committee at a cost of more than $100,000--most of it coming from the DNC.

McCain Meets With GOP Gays

Sen. John McCain (R-Ariz.) emerged from a meeting yesterday with the Log Cabin Club, a gay Republican organization, with his already strong chance of getting an endorsement even stronger.

"The senator really reached out to us," said Kevin Ivers, the group's communications director. He relayed that during the meeting McCain looked at Rich Tafel, Log Cabin executive director, and said, "I just want you to know, Rich, that I am unashamed, unembarrassed and proud to work with you."

McCain and Texas Gov. George W. Bush are the only GOP presidential candidates who have a shot of winning the Log Cabin group's support. "There is still a chance for Bush," whose campaign has agreed to meet with Log Cabin leaders, although McCain has been more outspoken in his opposition to discrimination, Ivers said.

McCain has so far won every straw poll measuring support within the organization, including one at its national convention as well as among individual chapters that have held a test vote.

Staff writer Thomas B. Edsall contributed to this report.

CAPTION: Hillary Rodham Clinton and Rudolph W. Giuliani are both launching TV ads outside New York City.