Lisbon is great, very compact and with good public transport (trams and underground). Go out to Belem for the monastery, the descobrimentos monument, and the famous pastéis de nata (custard tarts)
Go up to the alfama district for fado, and the quaint cobbled streets, then the castle at the top (it's quite a climb so comfy shoes are a must)
You can go to Sintra by train, lots of history and architecture there
The city itself is full of little streets with quirky, independent shops, fascinating to just wander round, and the food is great. There will probably be a fireworks display on New Year's Eve, and the Portuguese tradition is that you eat 12 raisins at midnight, for luck in each month of the coming year
The hop on hop off tourist buses are a good way to get your bearings, and pass the gulbenkian museum and the aquarium
I love Lisbon, it's a really friendly city (I live in the Algarve so it's relatively nearby for us!)