From a design point of view, you have some interesting options.
I have some questions.
Is there, or will there be, a finished entertainment space in the basement, accessible through those sliding glass doors at the existing patio?
Is it a living room/kitchen area that opens out onto the existing deck?
What I'm trying to get a feel for, is how your entertaining will flow from the upstairs to the basement.
Obviously, stepping areas down the slope will connect the two.
I would create a second level of deck, a couple of steps or so, below the existing one, and make it a place for the hot tub, taking advantage of the view and proximity to the forested area nearby. This would still be close enough to the existing deck and lounging and dining areas I would create there, so that all could be served by the kitchen.
Then steps would wind down the slope to an upper patio area with a water feature incorporated into it. This feature would begin near the existing upper deck, wind around the hot tub portion, to a pool created at the upper patio. It could then overflow and flow down to a second, but smaller pool at the existing patio.
This would connect all the levels and you will have created a cascade of living and entertaining spaces. Special care should be taken with landscaping this whole area.
The design of the pool is something to think about. The old fashioned finished looking pools are kind of passe. Now, a lot of people try to create pools that look natural in the landscape. They create plunge pools or lap pools or pools that create their own current for swimming, but edge them with boulders and water plants and such. You can make it look like a water course, draining down your slope with a pond or two.
Bill