IMO, you want to install the inverter close to the batteries. Voltage drop is more an issue with 12v lines than with 120v lines. Installing it further away requires bigger (and more expensive) battery cables.
I then pulled my distribution panel out and installed a Xantrex Automatic Transfer Switch on just the circuit that the outlets were powered off of. I ran an extension cord through the under belly and up into the bowls of the RV to power the transfer switch.
What's nice about this is that the outlets automatically become hot when I disconnect from shore power (assuming the inverter is on, of course).
I documented it here:
https://learntorv.com/inverter-basics/