Keep the first month simple. Book a place for the full four weeks rather than moving around, so you can build a routine: a café you like, a gym, a supermarket. Most first-timers try to see everything and end up tired; the ones who stay longest are the ones who treat the first month like ordinary life somewhere new.
Make the arrival boring on purpose. Book a flight with a good arrival time, and a fixed-price airport ride, for example with Welcome Pickups, so you don't have to work out transport while tired. Install an eSIM from Airalo or Saily before you leave so maps work straight away.
In the first week, a walking tour is the quickest way to understand a city's layout. WeGoTrip has self-guided audio tours you can start any time, and a city pass from Go City can save money if you plan to see several museums. If your apartment isn't ready when you land, Radical Storage can hold your bags for the day.