Is the car "new to you"? If it isn't, has the pressure been like this before (I'm guessing no)? If it
is new to you try and contact the previous owner and get an answer.
Your oil pressure will always be higher when you start the car than after it has been running because the oil is cooler. Cooler oil is more viscous and will result in a higher pressure reading. As it warms up it will thin out and the pressure should drop. What weight oil did you use? Nissan recommends 5w30, a thicker oil will also make the pressure higher than normal. Even though 120psi sounds high it's not unheard of.
Here's a link from a similar situation from three years ago.
It could be something as simple as a stuck gauge or a bad oil pressure sending unit. To check your your sending unit turn the key to the ACC position,
Do Not Start the Car - the oil pressure gauge should remain at ZERO. If it shows any reading when the engine is not running then you know where your problem is.
Make sure to check your oil before you start your car...
1) It gives you an accurate reading from a cold oil temperature.
2)
If you were running excess oil psi there is the potential of a leak, better to find out before you start it up.
Keep us posted about what's going on.
And welcome to NICO!