You want to ask youself why you are limiting yourself to just Tudor City. It is no doubt a charming area but super tiny apartments. I would consider broadening up your search to see what else you can get for your hard earned money.
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I have shown units in Tudor City. There are pluses and minuses. It is a bit of a hike to the subway because of how far east it is. On the other hand, it is reasonably priced. The buildings tend to have small units and the kitchens are particularly small and against one wall as opposed to enclosed. Some units that hit the market have not been renovated in a very long time. The studios in particular are very small. There is only one building, the last built, to have rooms that are a little bigger. Many residents like the sense of community and do not see it as isolated. There is that vacant lot between one building and the river, and there is always the possibility that the river view units could get their view blocked if something tall goes up. But overall, very good value. I would not go by the advice below that you can always rent it out if you want. These are co-ops. Though there is the ability to rent the units out, I know they do charge a sizable fee for the priviledge of permission to do that. In fact, they get a decent amount of revenue from those charges
Hope this helps.
Halstead Property, LLC
Bond New York