Cool strategy. And the local good food you can always find in a local good restaurant. To eat out there or to buy take away food too.  A good grocery store in a neighbourhood can never do any harm for sure.

And I disagree - I'd rent the best available apartment. Otherwise what's the deal - you work and toil for what ? To save some more or to make a great choice for temporary lodging. I take the second option  - this way each my trip is a cool adventure.