I think Wikipedia describes this the best….
Moderates within the GOP tend to be, to varying degrees, fiscally conservative and socially liberal, though there are others who are socially conservative and fiscally centrist. While they often share the economic views of other Republicans – e.g., balanced budgets, lower taxes, free trade, deregulation, welfare reform – moderate Republicans differ in that they may be for some gay rights, abortion rights, gun control, environmental regulation, federal funding of education, fewer restrictions on legal immigration, and for some, more relaxed enforcement on illegal immigration, abolition of the death penalty, civil rights laws, legalization of drugs, stem cell research, anti-war policies, or any of the above. Deficit spending is a highly contentious issue, within this faction as well as outside of it. Some moderate Republicans criticize what they see as the Bush administration’s military extravagance in foreign policy, or criticize its tax cuts. Others may support deficit spending, but feel it ought to be more directed towards social projects. Still other moderate Republicans are more centrist in their fiscal policies, in the tradition of Nelson Rockefeller. Concerning foreign policy, moderates may be less interventionist than neoconservatives, or place greater value on multilateral institutions. Moderate Republicans have seen their influence in the Republican party diminish significantly since the 1990s. Once commonplace throughout the country, today moderate Republicans tend to be found in elected office primarily in the Northeast and the West.
Examples of moderate Republican Governors include George Pataki, William Weld, Paul Celluci, Jodi Rell, Jon Huntsman Jr., Jim Douglas, and Donald Carcieri. Current U.S. senators include Susan Collins and Olympia Snowe of Maine, Mark Kirk of Illinois, Lisa Murkowski of Alaska, John Hoeven of North Dakota, and Scott Brown of Massachusetts.
Moderate Republican organizations: The Ripon Society, which was founded in 1962 as a group of liberal Republicans, today it provides forums for centrist Republican and their ideals. The Republican Main Street Partnership is a network supporting moderate Republicans for office, while the Republican Leadership Council is similar in direction. Former New Jersey Governor Christie Todd Whitman founded the Republican Leadership Council PAC in order to promote moderate Republicans for office. The Republican Majority for Choice is a PAC of and for pro-choice Republicans, and is often allied with the moderate branch of the party. Former U.S. Senate Majority Leader and 1996 Presidential nominee Bob Dole has supported the “Main Street” Republicans. John McCain has been considered a moderate Republican for much of his Congressional career; however, he moved considerably to the right on many issues during his unsuccessful 2008 presidential campaign.