Advanced two player rules clarification for 7 Wonders
According to the rules, the free city can take any action a 'normal' player can take with a restriction on discarding cards for money. The free city CAN build a wonder. In fact, a good strategy for the third city is to use it to bury cards your opponent might want, e.g. by building the wonder.

The free city CAN also discard a card for money, but only if no other playable card is available. Therefore, if the city has no playable cards, you can choose a card to discard and the free city gains the coins.

(Rules are here: http://www.rprod.com/en/7W-rules.html)