Where in the ideology do republicans and democrats stand?

Good question. Ideology is, essentially, the way one thinks about the world around them. It is a collection of beliefs and world views. "World views" includes how you think about your neighborhood as well as how you think about the world.

Republicans and Democrats are members of the dominant American political parties and choose their affiliation, to some extent, on the basis of their personal ideology.

What you find out when you look broadly is that the ideologies of the two political parties are not different at all. Both believe in the "American Dream." They are both comfortable with the political institutions in the country. They both expect foreign policy to protect and extend American interests.

It is only when you look in a more narrow fashion at individual policy differences do you see any significant differentiation in ideology.

One might suggest that the issue comes down to the basic nature of man. Republicans see man as essentially evil and stained with original sin and Democrats see man as essentially good and imbued with the potential of godliness.

Two very different approaches, but on the larger questions not much difference at all.