Which view are you worried about? Street view or the view from inside your house? Do you need a gate for access between the front and back yards? If so…

I agree with the greenery suggesting. Most cities have higher allowances for plantings than they do for fences. Where is your house located?

In Albuquerque, NM. I'll have to do research on what can grow and spread.

Something like this maybe? If anyone know what this is please let me know. Or if anyone knows something else that would be nice and grows in NM. I don't know names of trees and vines. Please and thank you!

Go to a small nursery and work with someone there to select plants, shrubs, and so forth that will work with your space limitations and climate. A garden designer can help you select what will work in such a small space which is so narrow, it will probably be in shadow a lot of the time. Make sure to integrate your landscaping and hardscaping with the street front of the house.

I take it yours is the home being constructed- to the right in this photo?

Which rooms face the smaller house to your left? What kind of privacy do you need? I.e. Bedrooms, bathrooms?

Do you have a view to anything you can focus on? If so, do that! Direct furniture, artwork, etc elsewhere.

If both houses just have bedrooms facing each other, you might not need anything more than good curtains and blinds.

tall evergreens (if they grow in Albuquerque) would be nice. I'm sure the neighbor would like it too.

You must have a yard, too. It looks like there's a view out to the back. Build a pergola with privacy screens. You'll be fine. It's a neighborhood!