I'm considering a 1031 exchange out of New York to a property closer to my location.  Does anyone know if states, especially NY, "honor" the tax deferment of a 1031 exchange?  Or will New York immediately, or sometime...

There are many qualified accountants on this message board who specialize in real estate taxation that may be able to serve you.Since you previously done your taxes using HR Block/Turbo Tax - the accountant you choose should first look at the previously filed returns to make sure they were done accurately. 

Welcome to US taxation!

The best entity for legal protection may be the worst for taxation for example.You definitely should get a local lawyer.

There may be important distinctions with local and state regulations as well as how the IRS treats the income and taxation of the property which requires different tax strategies.

@Chris SeveneyRegarding the accounting/taxation of the fund - you want to make sure the accounting firm has the knowledge and capacity to take on the work.Does the accounting firm know answers the to the following questions.Do they specialize in partnership taxation -Do they know how a partnership return is impacted if there are foreign investors, tax exempt investors, individuals as investors, entities, etc.Do they know how to deal with the taxation of the operations - If this is a real estate fund - do they know the in and outs of 1031 exchanges, how different items are depreciated, 1250 property, 1245 property, bonus depreciation, section 179 expense, etcDoes the fund operate in multiple states - are they familiar with the various state tax laws.Will the fund allow composite return to be filed in behalf of its investors - does the firm know which states offer composite returns and in behalf of which entity types they can be offered for.etc etc etc

It has to do with understanding of real estate taxation - something your current CPA apparently lacks.

But as I had mentioned initially, preferably it would be great to avoid the taxation all together. 

You might get double taxation. 

It's my understanding that you cannot live in it, either the one you're selling or the new one, although there are rules where you can 1031 exchange but then years later, move in and convert it to a residence, although I don't know how that works for taxation purposes.