The toughest part of moving plumbing is the drains. To move the drain, the floor will need to be cut open, concrete removed down 12-18" and the drain line extended from the original spot or another closer line. Drain lines must slope towards the house exit. A few thousand depending on local labor costs, concrete costs, etc.

Supply lines may have not been installed yet saving some of that redux.

"How much work is it to rough in another area?"

Very, but ask your builder.

What @Jeffrey R. Grenz, General Contractor suggested, cut the slab and connect to an existing bathroom nearby, or being this a bar sink without breaking up concrete, etc you can use a remote sink drain pump.

This is a question for the builder it depends on many things we do not know about. Ideally I try to put plumbing close to each other so when there is an issue it is better to deal with

Things to consider is If the drain must go below the slab, then distance away from your tie-in point will depend on how far below the surface your tie-in point is. If you cannot/do not want to use an AAV then you would need to extend a vent up through the other floors. If your tie-in is nearby other plumbing, then you may not need to go under the slab at all for a sink.

I would suggest laying out a complete build-out of the basement that is flexible for as many scenarios as you may come across in the life of the home (not that you have to finish it completely according to this plan). It looks like you are set up for a bedroom to the right of where you want the wetbar, and there would be a large open space next to the stair in front of where you want the wetbar.

Thanks all! I spoke to our contractor today and sounds like it will be a very involved process to jack the floor to find the tie in pipe. 3000 to 5000 is the estimated price … for a wet bar sink that we will use once a while. I think we will forego the wet bar and convert the already roughed in plumbing to a basement utility sink instead!

You can still have a bar with a remote pump, it's being done this way in many situations to avoid cutting concrete.