Mila and Julien's lovely flat is in an extremely convenient location. Initially I preferred to stay somewhere between the two rivers, but once I arrived I was convinced we made the right decision - the old Lyon is much more charming (in my opinion).
There are lots of restaurants in the neighbourhood (we didn't try any of these but even if you want to go elsewhere most likely they're within walking distance), some really wonderful ice cream shops and you have convenient stores nearby. I also recommend the walking tour (part of Only Lyon city card) for this neighbourhood as you would learn lots of interesting history.