I have an outdoor meter socket with a 150 amp panel for the heat pump and just inside the house I have a 200 amp whole house service. Where is the best place to install this surge protector. I would like to put in the outside box under the meter socket.
From the Square D documentation on the surge protector I just installed for my panel:
Note: The SPD requires two adjacent mounting spaces and should be installed as close to the main circuit breaker, or main lugs as possible.
Extrapolating that, you will want to place the surge protection as close to the main feed as possible, which for you is your meter-main panel. If that panel has the space, you should locate it there.