The Going Away Party gig can be found in the Rancho Coronado area of Santo Domino, in the east of Night City. You will need to get into a 6th Street base, find someone that is inside, then get them out again.
You can get through this entire mission without being seen, or you can just go in guns blazing and take out all the gang members, whichever you prefer.
If you wish to take the stealthy route, there are two mains ways to do it. You want to avoid the front entrance, but if you crawl under the house on the right side you will find a small crawl space that will lead to a gap in the floor. This will allow you to enter the house right beside the stairs. Head upstairs and go into the room on the right to find the person you are looking for.
The alternate route is for people with the double jump ability. Climb onto the roof of the houses next door, then jump across to the 6th Street hideout. Go to the rear of the house where you can drop down on top of a porch. There is a hole in the wall here that will allow you to enter the house, and you can just go straight ahead to find the room with your rescue target.
He will be on the floor, surrounded by bodies as something appears to have gone badly wrong. You need to talk to him to wake him up, then get him out. Leave the room and head left to the stairs, then carefully make your way down to the ground level. Ahead and to the right is a doorway that leads to the garage with a car in it. Once you get there, you can jump in the car and speed off down the road to meet the Nomad smuggler who will take over the rest of the job.
You will need to be careful as you sneak through the house, make sure you distract the enemy in the main room on the ground floor before you go for the garage door, or else he will see you.