First trip in February

We are planning our first trip to Japan in this upcoming february after a long postponing due to covid. Would love some tips from others here! We have dates but no specific ideas while there yet. More specific questions:

Recommended budget per day based on general costs of food and lodging there?

Recommendations for places to go while generally trying to avoid touristy locales?

Train for getting around while there or is there a better option?

How important to study basic Japanese?

Thanks!