The Phoenician (Starwood LC outside of Scottsdale) has a huge iconic pool and the resort offers guided tours of its cactus collection/rock garden. Scottsdale and Phoenix have art museums, places to hike, etc.

For food and some sun, how about either Hong Kong (although weather can be drizzle and gray) or Singapore? Lots of Starwood places have good pools. Barcelona, Lisbon or Madrid would also be good choices, or you could rent a car in Spain or Portugal and go to a couple smaller places.

Good for your kid for not being interested in taking a rowdy spring break cruise or trip with friends to notorious places like Fort Lauderdale, Cancun, Aruba, etc.