So your international lite option: Canada
Things could change by the time you retire, but right now, the US dollar goes pretty far in Canada, especially if you are mainly paying rent, buying things second hand, and consuming services.
As an American citizen (I'm assuming), you may not have to worry about visa stuff if you keep your stays at six months or less. You won't be able to work in Canada, but that's not a problem for you. Of course, do your due diligence about visa stuff, I'm kind of extrapolating from what I know about Canadians visiting the US, and making assumptions that things are bilateral. In practice it's slightly more complicated, but Canada-US travel is relatively stress free compared to other international stuff.
If you are healthy, you might get away with not paying for health insurance in the US or Canada while you are abroad. Get catastrophic coverage for an emergency, and pay out of pocket in Canada if anything comes up. You might be able to get yourself eligible for Canadian health care if you stay long enough, but don't know what that entails for a visitor. Do your research.
There are fewer LCOL cities in Canada. Rents and real estate tend to be high compared to equivalent US cities, but if you can manage in NYC, you will figure out a way.
Montreal would be a tempting choice for a few months. Really cheap rent. Big city, cool architecture. Kind of foreign compared to most of North America. Good smoked meat, good strip clubs so they say (I'm pro sex work, but cheap, so my experience is limited). Horrible winters, good summers, and the city is the best in the summer.
Vancouver is a gorgeous city, I love it. Really nice, and fun. Mountains on one side, Ocean on the other. Tons of greenery right in the city. Great sushi and seafood, though if you eat out at restaurants like I do when visiting, you blow through your budget fast. Rents in Vancouver are super high right now. Forum user Zikoris makes Vancouver work on a low budget, has a
blog about it. Summer in Vancouver is gorgous. As far as winters go, Vancouver is considered moderate for Canada. Minimal snow, not that cold. But it's the PNW, so you know, shitty, rainy, and grey for long periods of time.
Toronto, as big a city as you are going to get in Canada, will seem small to you coming from NYC. Clean though for a big city by American standards (the level of litter and stuff in American cities annoys me to no end). It's home for me, so I probably don't have much to say, fun enough, just stay out of the suburbs. Stupid liquor laws, but guess that doesn't apply to you. Rent will be your big concern, but I think you can still find cheapish housing. My spreadsheets tell me when I lived there last in 2008, I was spending about $1200 a month, with about $700 of that rent (grad student budget). You can try inflating approximately, I don't know if that's still reasonable or not.
I'm from Toronto, and I'm tired of writing, so I'm going to pretend none of the smaller cities exist. That's part of the reason people from the rest of Canada hate Toronto. See all the international culture you can pick up while travelling to Canada, I bet you didn't know that :)