Noah,
That is correct. If the sun were to just become a black hole with the same mass as our sun (ignoring how it got that way, or if it would get that way), the Earth's orbit wouldn't change a bit. We'd all freeze to death, but that's a different matter.
Using the old g=GM/(r^2) to get the gravitational field, when the r becomes VERY small, the g becomes VERY big.
My ROUGH calculations are that if the sun were to become a black hole instantly (ignoring all blow off from explosions and stuff) the radius of it's event horizon would be about 1.4 to 3km... or to say less than 1-4 miles across the diameter. At the outer edge of this horizon orbiting objects would be traveling at about 2/3rds the speed of light, at the inner edge all objects would be stuck inside. Either way, nothing would escape the outer edge of the event horizon, but you could (if you had some incredible energy supply to provide all the heat, light,etc needed to support life) live in that 3 mile wide area with out noticing anything particularly weird about the space you lived in. Though I'm uncertain what radiation might be like in that area...
-OOG Michael Smith