Check in vs check into
 

Is there a difference in meaning between check in and check into a hotel or a hospital?

Yes. You can't check in a hotel (unless you're looking in the hotel for something). Same with a hospital. We check into these things (for a stay).

Check into means to register to stay:

I'm going to check into the hotel.
I'm going to check into the hospital.

Check in can be used when there's no object. This still refers to staying at a hotel.

I need to go check in first, then we can go out to eat.

Check in and check into have various other meanings as well.

check in (with someone) = to let someone know where you are or where you are going to be (or what you will be doing)
check in (something) = to look or verify something somewhere
check into (something) = to investigate something