Well here's a start.
My missionary work is helping existing evangelical churches here that may be struggling and desire help. If they don't want my help, that's fine. I'm not forcing myself on any of them. These churches are also non-denominational and so they don't have a large organization behind them to help out when there are struggles. Mostly this involves teaching/preaching the Bible (in Spanish of course). I've attached myself to a solid church in Arequipa and the brothers here are very helpful to me with my Spanish and have become a second family to me.
That answers another question in that I'm currently living in Arequipa, a city of nearly 1,000,000 people. However, right now I'm concentrating on my Spanish and ministry opportunities with other Peruvians from Arequipa as they make trips to other villages in the surrounding areas. Later I may take up a second home in one of the villages for a few months to help out in a more consistent and visible way in order to gain their trust. This will by nature almost require me to begin learning Quechua at some point in the next year or so.
Arequipa has a desert climate and is at 8,500 ft above sea level at the base of the Andes and specifically at the base of 3 volcanoes, one of which is still considered slightly active.
In the larger cities like Arequipa, Lima, Pucallpa, etc. there are always English language classes that are eager to have native speakers, such as yourself, come in and help out. Sometimes it's just to have conversation in English in order to put into practice the things they've learned in high school or college. You could also go to the local plaza at any pueblo and offer to hold a week or month worth of English classes for free and you'd probably never lack students. Almost everyone wants to learn English that I've come in contact with.
I've also been to Bolivia three times and Mexico a couple of times. It's interesting to see the differences and similarities between the cultures. And every place on your list is on my list also, including standing on the equator. :D So plan your trip and take it.
And whatever you do, remember every country will have it's specialty of food, so take your appetite. Go eat where the locals eat, even if it means risking a week of diarrhea. Medicine is cheap and you don't need a prescription. Just tell the pharmacist your symptoms and they will prescribe you something or if you need to you can visit a doctor. They too are inexpensive. Anyways back to the subject of eating with the locals. This will get you away from the tourists and you be able to see a little more of the culture that most people never see.
As far as my name goes, my dad always called me "Jefe" for as long as I can remember and it wasn't long before my brothers were all calling me "Jefe" also. When playing a car racing video game years ago with my nephew, my player name was "jefe." When I passed him during the race he yelled out with his incorrect pronunciation, "jeef just passed me. Who's jeef?" At this remark everyone broke out in laughter and corrected him. The next day I changed my name to "hefay" and I've been "the_hefay" ever since. And now you know the important stuff. :D