This design was meant to encompass not only your required features, but most all the extras too. While it may be on the higher side of your budget, I think it will create an exceptional space to entertain your guests and a great place for your kids to play. The pool is obviously preserved, and concrete is added under the patio cover, which connects to the pictured planter box. The hot tub (pictured model is not mine, and used only for demonstrative purposes) and deck is placed on the opposite side of the pool for privacy and to avoid large groups of guests gathering near the door. The sink is located against the house to avoid large lengths of piping. Most of the left side of the backyard is dedicated to the kids, including a sand box and wood-chip play area, which makes a great place for a slide (slide pictured is once again demonstrative only). The fire pit was placed on a sort of island to make a secluded area for conversation. The large planter box in the back is a great space for fruit trees (orange trees are pictured, but whatever tree you prefer should work just fine), and the entire fire pit border serves as garden beds. One bed is larger and expands towards the walking paths. Overall, I feel this design can be long-lasting, and has a certain style and intricate quality that is sure to impress.
