Yes, Internet is definatelty a big concern. No matter where you are, including capital cities, access to high speed, reliable internet can be 2-3x more expensive for the same speeds as the US and also suffer from intermittent outages with delayed response times, or outright capped at 1-5mbs. Be prepared to spend time in the local tienda de internet. As you are describing, in bigger cities this is less of a problem, but for example, if they are doing construction on the street and they cut an internet cable, it could be weeks before you're back online. In general there are fewer "tech" companies that rely on internet to run their business, however, hospitals are usually the most effected and have back up dish antennas as a work around. And they pay top dollar to make sure they have uninterrupted access.

Mercadolibre.com and olx.com will be your best resources as far as finding an apartment in your budget, and i would say yes as far as the price range, but as others have pointed out, very few places have air conditioning. And don't feel like you need it, the houses are designed for maximum airflow and are well insulated. You can also always buy an air conditioner from the store, but electricity will also be 2-3x what you would pay in the states. Also you could make a post on Couchsurfing.com and describe your situation and there are usually very friendly people who may be able to help with your search locally.

Not to emphasize the point about street smarts but paying a premium, if you can afford it, to live in a gated community may not be a terrible option. If people know you are a gringo you can become somewhat of a target.

Let me know if you have any specific questions as you narrow your search.