gross4160 said: The tarp covers a grill which will be moved onto the patio.
Good! So, if you go for one of the trellis ideas, it can be as close as 1' from the wall. Or whatever is a convenient distance for the plants you decide on. Lots of decisions to make there - vegetables or flowers or both? Pockets, shelves or climbers? Be a good idea to look at arrangements other people have made and see what appeals. (just google 'garden trellis images')
When you say "along the sides" do you mean along the sides of the patio or along the property lines?
I don't know where or how big your patio will be, or what it's made of and looks like, so I can't say anything about that.
I meant along the property lines. It's good that the fence is already there, but it's not a beautiful one, is it? Could use morning glories or Kentucky Wonder beans or sweet peas climbing on it... maybe interspersed with a few tall hydrangeas, hollyhocks or dahlias... with a couple of skinny evergreen shrubs to break up the pattern.
The fence that looks like a wall of popsicle sticks along the back is crying out for some color and texture. Children's art, lawn furniture and umbrellas, a row of containers growing tomatoes and peppers, a children's jungle-gym - or something!
The lawn looks pretty scraggly. More than just winter scraggly; it probably needs help.
And yes, there does seem to be room for one or two moderately sized trees.
That place looks to me like a blank canvas on which a little imagination and a lot of spadework could create magic.