The Colonial center of Quito is the number one priority if you visit Ecuador.
You will enjoy the atmosphere, the shops (very local), ... plus if you have time you will discovery all its treasures hidden in the churches, museums, small bars and a couple of typical restaurants.
As in any major town, be carefull. Limityoupersonal belongings to a strict minimum, do not go outside the centre. It is safe but you never know.