one week in ecuador

But why not do Cotapaxi on the way to Banos or on the way back and then to Quito? That would save a double back from Quito.... Pity you haven't got time for the Quilitoa Loop or part of it....

yes, i m very confused about this

The above was just a suggestion. I think you are using public transport and when you say you want to visit Cotopaxi I guess you want to do the hike to the glacier, but maybe not. The refugio and glacier of Cotopaxi can’t be reached by public transport and it is also situated at a very high altitude 4800 metres and 5000 metres, so it is good to have stayed at higher altitude for a while before going there.
You could stay somewhere closer to Cotopaxi for one night and do a tour from there, and then continue to Baños or Quito in the evening. Personally I would feel that would be rushed and I would stay two nights. There are several lovely haciendas in the area from where you can take daytours. I have stayed at Hacienda Los Mortiños and from their restaurant the view towards Cotopaxi was stunning.

ok dear snowflakes so what would u suggest us to do if you consider that we'll use public transports'

how is our money situation/ can you afford a hacienda or are you really on a hostel budget? a hacienda would be a lovely experience though... pardon my lazy typing without capitals but very early wednesday morning here and i am very tired...

we r on a backpacker budget

As you are on a backpacker budget and don't have a lot of time in Ecuador, I think it would be convenient to take an organised daytrip from Quito to Cotopaxi (and hope for nice and clear view of the volcano). It can be convenient not changing hotels too often and if you do the daytrip in the end of your visit you are more acclimatized to high altitude.

A good budget place to stay in, in Baños is Hostel Chimenea: http://members.virtualtourist.com/m/p/m/2137d1/

thank u so much snowflakes
so, how would you arrange our itinerary now that you have a wide view of what we wanna do?

See my "Ecuador tips" posted 12 months ago. Best tip: Stay at Hosteria San Carlos 10 min. from Airport, and avoid heading into Quito.
Unless you are intent on seeing a historic colonial new world Old Town I would avoid and even skip Quito all together. It's just a huge
urban sprawl. You might include Mindo, and Otavalo. Make sure you allow one full day to take the tourist bus down the mountain below banos. towards Puyo. Wonder views, zip line. waterfalls, etc.
Rics

Born2travell, I don’t think I have a wide view of what you want to do. You are a budget traveler and you are going to use public transportation. However, I don’t know (even if I asked) if you have seven full days in Ecuador or if your week is with arrival and departure day. It will make a big difference.

In your posts above you have not really told us what your interests are. You said you wanted to visit Quito, Baños and Cotopaxi, and when you say that I presume that you like adventurous outdoor activities. Baños is a touristy place, but there are lots fun things to do; cycle along Ruta de las cascadas to Puyo, zip-lining, canyoning, bridge jumping and so on, but also thermal baths and massages. Above I included a link to my travel page about Baños, where I have written a lot of tips about what to do in Baños.

If you like hiking more than the activities that you can do in, and around Baños, I would recommend you to go to Quilotoa instead (leaving some luggage in Quito). Then, the next day hike to Chugchilan, and then the next day hike from Chughilan to Isinlivi, from where you can go back to Quito.

My travel tips and photos about those places:
Quilotoa: http://members.virtualtourist.com/m/3fbdb/1839f3/
Chugchilan: http://members.virtualtourist.com/m/3fbdb/184ac
Isinliví: http://members.virtualtourist.com/m/3fbdb/184089/