It is unlikely that you will get an apartment for 4 days only. Most apartment rentals are for a minimum of 7 days although you may get lucky.
There is a paucity of low cost hostelries close to Meia Praia.
You could have a look at Dom Pedro Meia Praia Beach Club Hotel. This is right on Meia Praia and has been having some offers recently.
As regards Dona Ana there are several guest houses in in the area.
The Montemar Hotel Lagos is about 10 minutes by foot from Dona Ana but is also 10 minutes from the town centre on foot. It is a budget type hotel.
Also have a look at Sollagos Apartamentos Turisticos, near the Montemar.
