Forgot to add picture 😅

I'd leave the basketball hoop in the driveway.

think about the light in the R side window, if you cover it, will it affect the room lighting?

you already have a covered dining area, I would add the pergola on that side... it's nice to have a cover over the cooking area for intense sunlight on the grillmaster. It's nice to leave a sun filled space for days when you need some sun and warmth.

Following is a link to view our patio and adjacent landscaping. The pergola anchors the space however we have several spaces within the area. Our patio is 26 x 24 with an additional 8 x 12 space which once held a hot tub, now a bistro table. Pergola is 8 x 12.

https://youtu.be/yh0ZL-PwsMQ

Without knowing the size of the table, number of people regularly eating, I’d put my dining furniture under the covered space and move the lounge furniture outside on the right side of the patio, the grill set up outside on the left corner by the grass. And I’d buy a big black and white striped umbrella to shade the lounge as needed.

I would put the pergola adjacent to the covered area you have now. Skip the basketball hoop- you’re risking your windows if you put it on the patio.

If you plan on having pots and flowers in that space, definitley skip the hoop - the basketball will damage everything (guess how i know 😅) - its a big patio and likely needs to be divided into zones based on how you want to use it - dining versus lounging versus conversation area - i would start there, dividing the space with outdoor rugs and oversized planters

Why do you want a pergola?  Is it to provide shade?  Of course the direction your patio faces and the time of day come into play, but typically  you should cover at least three feet more than the area you wish to shade. The problem is that pergolas are usually the depth of the patio because that's aesthetically pleasing.  Be aware that if you plan to place furniture near the edge, those sitting there will not be in the shade.