What is a neocon of today exactly?What are you?
Many neocons come out from Trotskyite backgrounds or the parents did. Their main philosophical influence is Leo Strauss.
They maintain one aspect of their former Communist views: a strong belief in international and "permanent" revolution. The revolution is no longer a Communist one, however, but a democratic one spurred by the great power of the United States.
They very much favor an interventionist foreign policy, bases throughout the world, and regard TR and FDR, as great heroes. They are very optimistic that United States can reshape the world and make foreigners into good democrats. They will use the UN if they can as a "tool" but will oppose it opportunistically if it refuses to go along.
In domestic policy, they don't like the "overreach" of the welfare state (as embodied by the Great Society) but embrace its essential premises as embodied in the New Deal. For this reason, many were initially involved in the presidential campaign of Scoop Jackson, a committed New Dealer).
Neocons are not particularly religious (many are atheists) but believe that religion is a necessary part of a "noble lie" (to quote Strauss) to keep the masses united in an agenda of "national greatness."
Irving Kristol, the godfather of neoconservativism, has a pretty good description from 2003 of what the terms. Unlike many neoncons, Kristol never tried to abandon or hide his beliefs. To his credit, he was proud of the word and defended it.