Thank you, Lax. I think the company caps the trip at 10 grand if that helps with budget. I'd be willing to fork in a few more if worth it.
So the hotel I linked ran us about $600/night, and normally would've been about $1000/night for the room we had. It was a legit 5-star hotel, and you get what you pay for. I was probably the poorest person staying there. On their premises they have a Michelin 2-star and a top 5 dining experience of my life. I've eaten at a lot of 1-star and 2-star places around the world, and this place earned its ranking. They also had the best gin bar I've ever been too, hands down. Private beach club and a separate 1-star restaurant in a cliff overlooking the Mediterranean. Lots more details I can PM you if you're interested.
What I will say is that I do not think Capri would've been great if it we tried to do it on a budget. Like I wouldn't go there and stay at a 3-star hotel. If you're in it to do great food, day trips to coastal places, rent a boat, etc. it's excellent... very indulgent place, and you can make it very relaxing or very adventurous or a little of both. And you avoid a lot of the touristy issues of the rest of the Amalfi Coast outside of certain parts of the day in certain areas. So if you want to go all in, I'd recommend it. If you think you have to stretch too much past your $10k budget to make it work, I would go somewhere else.
International trips I've taken in the past 10 years include 2 weeks in Ecuador/Galapagos (Silver Seas cruise), 2 weeks in France (Paris/Loire Valley/Provence), 3 weeks in Italy/Switzerland (Rome/Umbria/Tuscany/Venice/Lake Como/Lugano), 2 weeks in Italy (see above), a week in Belize (twice), and a Spain trip. The Galapagos was the most unique put-those-photos-on-Instagram place I've been, Capri was the most luxurious. But they all had their positives and negatives.
We travel a lot because we don't have kids at this point and my wife works internationally. She worked in Rome for awhile, and now she works for a global hotel company that sends her lots of places (for example, she is about to embark on a trip to Dubai, Shanghai, Barcelona, Cabo, and some other less exotic locals over the next two months for work). So we have a pretty good grasp of most travel hot spots at this point, especially in Europe. I'm blind to places like Fiji, Bora Bora, Turks and Caicos, etc. because that's not our type of trip. Likewise, I think Hawaii is overrated AF.
Planning the right trip for you on a healthy budget of $10k is all about having goals and picking the right destination/lodging/activities to realize those goals.