I suspect that the Lagos area might be of interest to you.
Apart from Tavira, it is one of the only coastal towns in the Algarve to retain its traditional Portuguese Character.
There are two good local beaches - Porto de Mos and Meia Praia, both of which are ideal for kids.
Assuming you have a hire car, the coast west of Lagos is rugged and beautiful with some small villages and great small hidden beaches.
Checkout also Salema.
