I'm thinking about spending two weeks in Ecuador in August. Hopefully, I can climb the big four or five volcanoes. Since I live in the North East, acclimatization is a lot important, so I'm thinking a schedule close to this.
Day 1 - 2, arrive in Quito and relax, some sight seeing to help the process.
Day 3 - 4, climb Iliniza Sur/Norte
Day 5 - 6, climb Cayambe
Day 9, rest day
Day 7 - 8, climb Cotopaxi
Day 10, rest day
Day 11 - 12, climb Chimborazo
Day 13, rest day back to Quito
Day 14, fly home
While I do want to climb as much as I can, I can skip a few volcanoes if needed, but I definitely want to do Cotopaxi and Chimborazo. So, what does everyone think?

Too aggressive, I think. On your 2nd or 3rd day in Quito, you could go up the Teleferiqo which is fun in a silly sort of way and takes you up ~13k ft (I think) on a tram. Then I'd try to get at least one ~14 - 15k mountain in before Norte. Lots to choose from (Pichincha, Corazon, etc.) Not clear from your profile if you ice climb. If not, then skip Illiniza Sur and just go for Norte. If yes and you want to try Norte and Sur, you'll need 1 - 2 extra days for that (3 - 5 days total.) If you are really going for the big volcanoes, you could skip the Illinizas entirely. After your 13 - 14k mountain, do a slow (3 day) ascent up Cayambe (starting day 5 or 6) as your final acclimatization.

I assume you're going unguided? If yes, one thing to keep in mind is that you need to prearrange transportation and it's sort of a pain in the butt. It's tough to change around due to weather, etc once you get going. Ecuador weather can be sketchy so unless you're lucky, you may end up constantly turning back and not having that one extra critical day for the weather to clear because you have to catch a ride. The first time I was there, we put in loads of padding and still ended up not getting up anything due to weather.

That's very close to the scedule that we did, but we planned 0 days in Quito and went to Pichincha. Since we already live fairly close to the same altitude as Quito, we didn't think staying there would be of any benefit. We were supposed to do Pichincha (as Sophia suggest) on day 1, but I got food poisoning in Houston on the way down and completely missed out on Pinchincha and Illiniza Sur.

Although our scedule was aggressive, we already mostly knew what to expect altitude wise because we had already taken several trips to similar altitudes. One thing I can tell you for sure that if you are not acclimatized you will be miserable. If you have not been to similar altitudes before and don't know how your body will react (remember that physical fitness has little to do with acclimatization) than you're scedule above is too aggressive. If you already know how your body reacts than you may be OK.

Don't underestimate the altitude and don't rely on physical fitness. When I did Cotopaxi, at the beginning of the climb I was clear in back. However, as time went on, we passed a lot of the faster climbers while they were slumped over and puking along the climb because they were not acclimatized.

You won't even have a good time if your not acclimatized, so it's pointless to climb any peak when you are not. The more acclimatized you are, the better you will feel and not being acclimatized is just dangerous.

The more lower peaks you climb first, the better off you will be.