Agree, wrong palm, wrong place. Can you back away and show more of the house above? Does the second story step back from the footprint of the ground floor at all?

Igo, do you have any preferences: palm family, evergreen, conifer, deciduous? Color? Flowering?

How wide is the window area you'd like to conceal? (Consider that the view may be at an angle, rather than perpendicular to the windows: how broad does the new tree/shrub need to be to provide privacy? Would multiple narrow shrubs or trees be acceptable?)

How tall is the fence? Can the neighbors see over the fence, perhaps from windows?

How much sun would this new tree/shrub receive when it is still young and short? What direction does that side of the house face?

Run, the triffids are trying to find your back door!

Second story window steps back from the footprint of the ground floor ~4ft. So distance from the tree center to the window ~10ft.

I do not want palm or conifer. I have a lot of conifers around. I consider evergreen and deciduous trees. No preference about color or flowers. Prefer without messy fruits.

Window on the second store is exactly in the front of the palm and about 8ft wide. I think 8ft wide tree would be enough to provide privacy. Multiple plants are acceptable.

Fence is about 6ft tall. Neighbors can see our second store window from the ground and we can see them from window.

This side of the house faces north-east direction. Small tree would receive sun only in the morning till 12pm.

I really like using the narrow growing Hymenosporum flavum, or Australian Frangipani for such a sideyard screen tree. Fragrant flowers, no messy fruit, relatively no messy leaf drop, fast growth and year round good lts only fault is its not good in windy locations.

You might also consider Agonis flexuosa 'Afterdark', Tristania laurina, or a narrow clumping bamboo such as Bambusa glaucescens, 'Alphonse Karr', or Otatea acuminata aztectorum. The tree Daisy, Montanoa grandiflora also makes a nice narrow vertical screen with colorful flowers blooming now through January, and flowering shrubs such as Iochroma cyanea can be used to similar effect, but can defoliate if you get regular frost.

Love the suggestion of Hymenosporum flavum.

I'm working on project with somwhat similar conditions in the Bay Area ( they want their 2nd story bedroom window screened )

We're considering Rhamnus alaternus - Italian buckthron. You can shear the bottom branches into a hedge or clip them right off so that the plant becomes a standard tree.

Eucalyptus ficifolia - its one of the smaller Euc's . but the pinkish red flower stamens do tend to accumulate on the ground below during the long blooming period. The canopy can be controlled but left untamed it can get as wide as 15-20 feet with age.

Acacia cognata is a fast growing weeping shaped tree. Its an evergreen so does shed some all season long. I have one in my back narrow 15 wide yard and enjoy it very much for its screening and foliage effect.

Acacia podalyriifolia - "Pearl Acacia will grow to the 12 foot range ( so might not be tall enough ) but it is a beautiful little tree, - some litter from fallen flowers.

and of course there is the old standbys that most Californians turn to : Myoporum laetum and Pittosporum - you can usually find these in a well run/ horticulturally shrewd Home Depot such as the one in San Rafael -.... which by the way has some incredible HUGE beautiful 9 foot tall camellias jap. in 24 inch boxes last week at a v. reaonable price.

If you were still open to a palm I would suggest the simple but lovely queen palm - Syagrus romanzoffiana - I think it would be perfect in your particular area. It's a very low maintenance palm with a graceful shape .

Thank you for your advice.

I have decided to plant Hymenosporum flavum. It looks very nice on pictures.

Where can I buy it in the Bay Area?
I am in Palo Alto.

Its improper position is quite apparent. And as of now I am not having any idea that where you will get Hymenosporum Flavum, trying to gather info about it, will let you know if I get to know something.

It is available thru several wholesale growers; San Marcos Growers and Pacific Nurseries both have it. You can ask your local retail nursery to order one for you.