Immersive First Person Settings changes the in-game, third-person camera view to a more realistic, true first-person experience. Enhanced 3rd Person Camera is a good, free alternative to IFPS, although it was adapted from Skyrim. Immersive First Person Settings was explicitly developed for Fallout 4. You can also try Survival Options Mod. 

Another alternative adapted from Skyrim is Custom Camera. Custom Camera adds more features and functionality, but as a fully realized plugin, requires modding knowledge and familiarity with manipulating game files. Immersive First Person Settings only requires you to replace an existing INI file with the one provided. 

Reduced camera clipping

Previous renditions of this mod and similar plugins have suffered from a clipping issue. This meant that if you turned your character’s head too sharply or too far down or up, you’d likely end up looking inside your character. 

Similarly, if your character were to stand too close to a wall or other structure, you would sometimes be able to see through that wall. Immersive First Person Settings changes this all by removing most of the view clipping problems. You can now move your head around without your view being obstructed by your own character. 

Now you see me

To increase the sense of realism during gameplay, you can now see your body, legs, and arms while moving through the simulated environment. This is an improvement on previous attempts at first-person cameras, where your character felt more like just a floating head or lone camera. 

State-based automatic camera switching

SACS is a further enhancement of Immersive First Person Settings. You can now seamlessly and automatically go between the optimal first-person view for interacting with the environment, which is expressly set up for combat. Simply draw or holster your weapon to move between the optimal camera setups.

Well-rounded camera settings

IFPS is designed to change your camera view and make you feel more a part of the world. A specifically dedicated automatic combat camera with SACS and reduced view clipping are two features that make this possible. You can now view your character through a first-person camera while still completely immersed in the environment thanks to visible body parts as you navigate your surroundings.