As someone who was on the road for three years, this was my biggest take away. If anything I'd treat one month as an absolute minimum. I'd prefer not to be anywhere less than 3 months. It ends up taking a week just to get truly unpacked.
From that base, you can still do day trips and weekend trips.
The amount of time maybe varies by the location and the visitor, but... how much do you carry that it takes a week to unpack?
Until I started travelling with my wife (and now a child too), one main lesson I learned was "you aren't going to need it" - every time I went travelling it was lighter than the trip before!
I had one carry on for clothing and a backpack for essentials and some electronics.
I guess more accurately it takes a week to get settled in. Most of that time isn't about physically removing the stuff from the bags but more about where you need to put it and what stuff you might need to go rebuy and organize, in the new country.
Sorry, I read that far too literally! Yeah, that's fair enough. I certainly needed large blocks of staying still, but didn't feel the need to stay anywhere as long as three months - month long blocks were more common for me.
From that base, you can still do day trips and weekend trips.