I lived with out a car for 4 years and biked from Wooster Square, then East Rock to work at the Yale Med School. I would get Groceries from Whalley Ave stop and shop and would stuff them in a ortlieb pannier. Most people would hate doing this but it wasn’t bad…my determined stubbornness was key.

East Rock might be a better bet since you can get groceries from P&M or Nicas. There is also better shuttle coverage which will help in the winter/snow.