The best place is The Lodge. There are two locations there where there is unlimited storage. In the basement where all the crafting stations are, there's a Research Station. Just behind it is a yellow storage box which has unlimited storage.
The second place in The Lodge is in your bedroom there's a large storage cupboard.
Your outposts can also be used for storage.
Also, increase the capacity of your ship or get a better ship that can carry more in the hold.
The best thing though is to ditch or sell all your rubbish items when you can to keep things manageable. Don't hoard too much.
Hope that helps