Building on Bianca´s comments it does depend on your traval plans. Since you come in October you enter the 6 month summer season where in my opinion the best choice is in the suburbs, where daytime activities are highly sought after, and it´s noticably cooler than the "cement jungle". Not to mention night time when you can go out readily here, PLUS take the train to town which can get you there in 20-30 min equal to or faster than within the city itself, especially nights out, where traffic is complicated to say the least.
For an "up-to-6-8-month-trip" I wouldn`t doubt recommending the greener, quieter, cleaner aired, suburbs, Such as La Lucila or Martinez where I live. Its full of apts near the station, and I see owners with dogs in all of them so it´s just a matter of asking the real-estate agent right in my building what they can find in the area, that is if you wish to know.
If you plan to stay year-round, well then it depends more on your personal situation. As a couple or family, this area still could be your choice, since you don´t need to go out that often and kids and dogs love having a garden. But as a single female (or male) it makes more sense to be closer to the "action" in the city, more so in winter, where its easier to walk in and out, and flag a cab anytime.
If you clarify your situation I can be of further assistance, such as asking a single female visitor who recently arrived with her dog, about her rental right off a major downtown park.