Which direction does the door face? No trees will mean BEATING sun so if you hope to spend much time lounging during the day you will need a cover of some sort. From where do you desire this view to remain? I really do not see how it will obstruct views if it's near the door..the windows there are not huge gazing windows..... The deer/privacy etc say the yard will likely get fenced at some point.....How much of that view do you OWN? Looks to be a new development, so it won't be long until your neighbors block much anyway....Whatever you do be sure you like it within the land you own...the rest will be owned by others.....

All good points, my direct view and direction from the door is the picture with the deer on it and our land stops at the top of the hill

What view exactly? I agree you are in type of subdivision so homes will block some view . I honestly need a lot mor einfo and pics from where you want the patio .. Do I understand the view is where the deer is??? I don't get it. Show us apic standing in the space where yo want to have the outdoor space so I can see exactly what view you want to keep.The house in the top pic is a very typical NA average home is that your house ? What on earth do you mean by European home design. BTW I have been to the place where the Sound Of Music was filmed not one thing like what you show. I really am confused so I need to understand a lot more .

I don’t mind covering the houses but I wouldn’t want to cover this hill and the trees/forest on the right. By adding a covered patio you risk that bc the hill steep. Adding a picture to help visualize the view I like

The open space and forest on the right is the view I like

Without a covered patio I can easily replace the flower pot holder with a nice barbecue/island but if I then got shrubs to add landscaping and privacy it will cover the hill which I like. Same concept with adding a patio attached to the home. If it’s not high enough it will cover the trees on the right. So the dilema is placing things in the right place and building the right height to still keep the open land feel