Some additional information would be useful to get suggestions. Are you trying to block the house from everywhere in the yard or mostly the view from the house or a patio near the house? Do you have ideas for how you will use your yard? That is, do you have kids who will want to use the yard for kickball or are you planning a future pool, etc. That will help decide where to best site the tree. Can you add other photos that show the rest of the yard and show the relationship of your house to the neighbor? (I can't tell if that is your house along the right part of the photo.) Sometimes a huge tree near the fence is less useful than a shorter tree that will give you a nice view and some privacy in the areas you are likely to hang out in the yard, and a tree closer to where you plan to be will block views sooner since it won't need to be as tall. Also, in many areas, any part of a tree that hangs over your property line may be able to be legally removed by the owner of the property it hangs over.

Visiting a series of reputable local nurseries (not big box stores) will often show you various choices and get local expertise. Or there may be a more regional forum here on Garden Web that can offer you more local expertise if you don't get responses here. For instance, I often look for information in the New England forum since that is my local area.

California? Florida? Texas? Arizona?

you are in a box.. you have to get out of it ...

first... a tree is said to be twice as big underground.. as above ...

second.. you need excessive height.. because you are insisting on planting at the lot line ...

i see the patio furniture... what you do ... is set it up as you might use it ... and sit down ... and think about the height of a tree planted halfway from your chair.. to the lot line.. using trigonometry.. you will note.. that a much lesser tall tree.. will give you some privacy ... while you are sitting ..

in the alternative.. you plant two trees... one over by the wall ... that will take a decade or two to get large enough to solve the issue there... and a second.. smaller.. more aggressive tree.. nearer the seating area ...

even if there is no patio/deck ... you plan the trees long in advance ... perhaps by the time they solve your issue ... you will have one...

need location for specific suggestions...

ken

I live in central California. It's hot, dry, and always sunny

well.. this MI boy can not advise as to specific plants .. except to say.. no stinkin italian cypress ... lol...

ken

Wow, so their yard is 6' higher than yours?

It would have been much easier if you had let that higher yard extend about 5' into your yard so you could plant some stuff up at that same height along the fence.

But stacking the fence right on top of the retaining wall...was really bad home design.

Your options are pretty limited, especially if you only want tall evergreens, yet no pines... The only slightly mitigating factor in your favor is that in Zn 9, some trees will stay evergreen.

Ya it really sucks. I guess i'll have to plant some small "patio" trees around my patio to block the view until my other trees get large. Trees in my area grow very fast b/c of the year round warm weather and very long summers. My mom has some form of a bay leaf tree that stays evergreen in her yard and it has gotten massive in just 5 years. I am about to pour a 23'x23' patio right where i was standing when i took the picture. I'm going to build a pergula on top of it which will block some line of sight and i can plants some patio trees around it for privacy. I am using the yard just for a nice hangout with family and friends.

I am using Eastern Red Cedar and Arizona Cypress to outline my property and provide some privacy from the highway. This is in hot dry Z8 Tx. I have seen both trees planted somewhat close to houses with apparently no foundation problems. Both trees tend to lean slightly away from the structures. Both of these trees look good and are drought/heat resistant.

Actually, I have the perfect tree for you...the LOQUAT!!!

loquat is remarkably drought resistant for a broadleaved evergreen
The loquat, an ancient fruit grown in Japan for the past 1,000 years, is
probably native to the cooler hill regions of China. For many years,
loquats have been grown as ornamentals in California, especiallly along
the southern coastal plains.

Loquats are normally bushy, rather dense trees. Their broad, leathery,
dark-green leaves are often used in floral arrangements. Easily grown,
attractive trees in the garden, they blossom and set fruit from October
to February. Selected varieties produce clusters of excellent yellow
fruit that mature in the spring and early summer.

They grow about 25 feet tall with a canopy that spreads 15 to 20 feet

They are dense evergreen shade trees of suitable size...and even bear tasty fruit on top of that! So, what more could you ask for? Go plant a whole row of them!

Another option is the Magnolia grandiflora...maybe you could throw one in the middle of the fence line too. But, I still think the Loquat is cooler! B)

Reaching 27.5 m (90 ft) in height, it is a large, striking evergreen tree with large, dark green leaves up to 20 cm (8 in) long and 12 cm (4.5 in) wide, and large, white, fragrant flowers up to 30 cm (12 in) in diameter.

Magnolia grandiflora roots are not good for retaining walls or near concrete. They are very beautiful trees but they get very large and have a very large root system.

The Loquat isn't a bad idea, actually, but unless you like the fruit, it's very messy and attracts rodents. The seedlings are also unpredictable in size and habit. There is a non-fruiting version that makes a good screening tree: Eriobotrya deflexa. Root damage potential rated as "low".

Eriobotrya delflexa information

Also look at Elegant Brisbane Box, which has a fairly vertical growth habit and also rated "low" for root damage potential
Elegant Brisbane Box

...One man's free fruit is another man's "mess?"

Western civilization sure is a curious thing... :D

That wall seems like a great location for a trellis. You could get some vines to climb it. Passion Fruit, grapes, whatever.

Arizona Cypress grows to 40' tall and 15' wide. Italian Cypress grows 40' tall but only 5' wide. Both grow relatively fast and are evergreen.

You have a lot of options, it really depends on your taste and how fast you want the privacy screen to block the neighbor. Leyland Cypress will do the trick, or there are several junipers and hollies that would work. Check out the photos of here for some more ideas. Privacy Trees For Screening