It's likely to be easier to make an advance booking somewhere like Sport Villa or Condo Chain.
While it is possible to look around for a house/apartment on arrival, you could end up spending much more time looking than enjoying your holiday - plus it could be more difficult to find a 2 month let with November/ December approaching.
And all the time you are looking is eating into the magic full month for a good deal. Just my view mind - but I'd rather have somewhere ready to park my bags straight away, with the option to have that base and travel elsewhere now and then. Two months can pass very quickly! Enjoy
