Difficult Combination.
The best beaches at Porto de Mos and Meia Praia are about 1,5 km from the Centre where the nightlife is.
You basically need to decide between somewhere near the city walls or somewhere near a beach and then compromise. For the kids sake, I would find somewhere near the city walls and then accept that you will have a longer walk to the larger beaches or accept that you will make do with smaller beaches closer to town such as Batata, Pinhal and Dona Ana which are likely to be very crowded at that time of year.
A final note: The ferry over the river to Meia Praia from the old town should be operating in in the day time at that time.
