I have been to all the places you listed except Rio De Janeiro. I have avoided it largely because of the outrageous visa requirements for Americans. Still, I have read that Brazil has a temporary waiver of the visa requirements currently. Still, I would not put is at the top of my list.
Cartagena, stopped there while on a cruise and did a nice local tour. It was good, but I would put it at the bottom of my list.
Didn't know there was a Moscow, POLAND, but, if you go to Poland, go to Krakow. Still, I would pick another on your list.
Two places you list would be among the cheaper to visit, that being Mexico City and Peru. Mexico is a very dangerous place in about half the country since the Drug Cartels virtually control vast areas of the country. Still, you could do Mexico City, just be careful where you go. I recommend taking a tour and not missing the nearby pyramids north of the city.
Peru would be a wonderful choice. Spend a few days in Lima and then take a tour of Cuzco, the sacred valley and Machu Picchu. It is amazing. We used Peru Agency for our tour and it was wonderful
Istanbul is another great place to visit, much to see there. Plan to spend 5-6 days there.
I would not go to Hong Kong, and fail to visit China. It is a long way to fly just for Hong Kong. It is an interesting city, but I would not pick it for your choice, since the city is expensive and the flights there would be long and expensive.
The Blue Lagoon is great, but if you go to Iceland, do more on the Island. We did the Blue Lagoon for a day and then a week long ring road tour. Still, Iceland is expensive.
Ireland is great and we have 10 day tour with Gate 1 Travel booked for July, cost is about $2000 per person.
In summary, I would recommend Peru as first choice, but consider Istanbul or Ireland as well.