For the cost of owning a home in any of those places (exclude the purchase price) you can fly or drive to all those places, stay in the finest hotel, several times each year. Look at taxes, utilities, insurance, home watch, maintenance, and home watch here while you're there. And because those three places are still many miles apart, will you still have the travel and stay expense anyway?
If it's a must do, pick one of those three places and buy a condo there. Pick the one where you know the kids wont move away from. And St Louis and Cleveland will be a lot less than NYC.
But definitely do a cost comparison of owning vs traveling. Travel is almost always cheaper.
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