One should be aware that while the weather in the Algarve in the 2nd week of October has been quite good in recent years there is no guarantee that it will be!
I would suggest that somewhere like Lagos or Tavira would suit you needs.
Lagos still retains its Portuguese charm with its old city walls, the old, town, its great cliffed-line coastline as well as great beaches.
If one wants to avoid hiring a car one should seek something near the centre of Lagos or on the route to Praia Dona Ana which is easily walkable from town.
the following sites may be of interest:
http://www.solpraiaferias.com/
http://www.holidayslagos.com/houses_apartments.html
