Palacio del Gobierno
You can't go inside the president's residence. However, you can see the Andalusian patios and fountains in the centre. They show a scale model of Independence Square at the entrance. There is also a placard which marks the spot where President Gabriel Garcia Moreno was assassinated with a machete in 1875 on the way from the cathedral to pray. He was a strong Catholic with many enemies. The tour guide tells me the current president (as of November, 2007) doesn't even live here.
Be careful when you want to make pictures of local people. Some locals do not like to be photographed.
So be polite and friendly, and talk to them first and ask if you can make picture.
Some of these Indian ladies are selling small Indian souvenirs, you can try to buy something and them you get more chance to make a picture.
(In fact Indian is a wrong word, it is better to call them Indigenas)
Remember: you are not walking around in a Zoo. These are also human beings just like you. So show some respect.
Another possibility is using a big zoom lens, and then you have the chance that they do not notice you when you are making the picture from a larger distance.
A Canon Eos 500 camera with a 28/80 lens for general use (scenery, buildings, . .) and a Canon Eos 300 camera with a 200/400 lens especially for local people, wildlife and close-ups. (+ Canon flashlight for indoor and at night)
The Central/Northern portion...
The Central/Northern portion of the city is the most modern, with wide avenues, modern buildings, stores and all that sort of useless and flattening stuff such as commercial centres, fast-foods and so on. The picture is an example.
There's a very nice bookstore at Juan Leon de Mera, corner with Veintemilla: Libri Mundi. It's worth the visit, you may find all the photography books you need from Ecuador and Latin America and also the normal literature production in Spanish. In face of the bookstore, there's a typical expatriate meeting point: an open-air coffe-bar which is tempting and relaxing.
Dance the night away to live Cuban Music!
This place is great. You might have to pay $4 to get in, but that will give you a free drink (mojito or cuba libre) and you get to dance the night away to live Cuban music! The music is great, and the people working there don't mind showing you some steps (trust me, they really know what they are doing!). The atmosphere is great and the crowed varied, but what you all have together is that you want to sweat the night away salsa dancing!!!
Open until 2am.