This one's a pain no matter what you do...it's caused by a limit in Revit, which has a 20 mile radius of accuracy away from a project base point. If you are trying to bring in site files, and the site files are defined at their real-world northing/easting coordinates, you have to move the site to Revit. It's not the other way around, so here's what you need to do.
First, if you're in Civil 3D our AutoCAD, make a duplicate of your site model drawing. In the duplicate, turn on, thaw and unlock any layers you want to include or manipulate. We need to have the contours, TIN, surface, existing and proposed structures at the least.
You're not going to rotate the site (we'll take care of this in Revit model by rotating a view). You're also not going to flatten anything - make sure the surface, existing building layouts, etc. are at their 3D elevation (BTW - if you're a plain AutoCAD user, and you're flattening sites to have no elevation, you're not allowed to play in this park).
Second, you're going to have move everything (yes everything) to 0,0 (not 0,0,0). Use a known point - like the corner of a proposed building, corner of a lot, etc. so that the model is within 20 miles of 0,0. That's why you want to open up all the layers - so you don't leave anything stranded, and out in spaces. One of our users adds a location marker that he uses as a reference, so he knows where he's coming from and going to.
Third, if needed, run the export to AutoCAD command from the Civil 3D application menu - this dumbs everything down to 3D models and plines - this converts it to non-Civil 3D objects while maintaining elevation. You only do this if the geometry doesn't come into the model as expected.
Another option is to create a rectangle around your site, and use the AutoCAD trim command to get rid off long linework that runs out into space - you're doing this if you have long lot lines, roadway profiles, etc. Keep it focused on the area of the site you're working on,and keep the model small.
Once you do this, you can use the Link CAD tool to bring in the file as a reference - don't import it, as these still get changed over the course of a project. We're mainly doing this for sites that have more than one structure or building - if they're small, it makes it easier to keep all items relative. It also helps to do your project this way when you have a lot of connecting components in a model, and are running pipe, etc. between the buildings - or connecting power circuits to panels in remote locations.
The CAD file will come in at elevation - so it will help you add your levels at the correct relative elevation to the site.
I'd include images, but since a lot of these projects I'd use are active, I need to refrain...but hopefully this helps you to streamline your workflow.