About Nerja: It's a nice coastal city with tons of history. You will see ruins from the old roman empire there and also from the muslims. It's famous also for the caves around the city, that seems to form a huge network inside the mountains, with tons of miles still unexplored.
About Alpujarras: It's the area of mountains and valleys surrounding Granada. It's a beautiful natural area crossed by tons of small rivers (some mineral water factories are found in the area). There is a small village there named Trévelez that is worldwide famous because the quallity of their Jamón Serrano (dry and salty ham). I have been there and it's curious to see all the buildings with drilled walls and full of ham inside. The drilled walls allow the fresh mountains air to dry the ham for months before it can be eaten. Probably they will show you that village or similar ones to taste the ham.
About the gift... for young people, usa brands t-shirts or caps are usually a good idea as are cheap there and expensive and trendy here. When i went to USA, i bought back surf/skate t-shirts for my friends and they loved them. For example Quicksilver, Billabong, O'Neill, Rip Curl, Dickies etc cost me there around $15 when the price here is around $50.
For the host señora... not sure what is typical in USA, post samples here and i'll tell you if could fit well.
Another thing that is always welcome could be chocolate. Of course we have all kind of chocolates here too, but with USA brands and English language in the envelop could be fun apart from tasty.
Related to USA food, you are going to notice a big difference in something as standard as Coke (named Coca Cola in Spain). The standard Coke in America is way more sweet than in Spain. I noticed a big difference in my trips to Miami and Mexico. Also we don't have as many flavors here. We have only standard, light and zero, not cherry or vanilla etc.
Where are you going to live finally? with a family? in a student's building? if so, only with other Americans? you said the place is named Angel Barrios but... there are tons of places named that way in Granada as he was a famous classic musician
If you know the address or more details, i can research about it.
About the clothes, don't worry a lot, clothes are cheap here in franchise shops like Zara, Pull & Bear, Springfield, H&M etc.
Looking forward to read your experiences here, i'm curious about how an American sees my country. Also as you are going to expend a few months here and you CAN'T MISS my city Toledo, we should try to schedulle a meet once you are stabilized in Granada and can plan your schedule and trips. I would love to visit Granada again as i haven't visited it since my bachelors party 3 years ago, but as my wife pregnancy is due in early November, we can't travel a lot now so if we meet will need to be here in Toledo.