If you want to party in the Algarve over the New Year you need to look at Vilamoura, Albufeira, Praia da Rocha (Portimão) and/or Lagos.
Faro is the regional capital of the Algarve. It is administrative centre and has a few sites of interesnt but I would not call it a holiday destination.
I must admit some bias as I live in Lagos, but I would strongly counsel against staying in Faro.
Most of the bars and restaurants in the centre of Lagos will be open and there should be quite a good atmosphere down town
If the weather is good, our beaches can be great for winter walks etc.
