Max 80-100 € per day and room. Traveling with a two year old.
Carvi: http://www.booking.com/hotel/pt/sol-e-praia.pt-pt.html?aid=306051 over 7 years ago
I guess you can avoid the south (too much touristic) and try a car trip by the south-west cost, beautifull and less expensive. If car is not an option, go to Lagos, or Sagres.
Important note, please do not go to Albufeira, Quarteira, Vila Moura. about 7 years ago