Unfortunately, there is no way to avoid capital gains on either of these transactions.
The latest changes to the NY Capital gains laws closed any loop holes that you might have.
For the medallion, all you can do is make sure you capture all the costs of maintaining and managing its value, increase the cost basis.
For the apartment you own. If this apartment was not your primary residence, you can not avoid capital gains tax, but you may defer it, by purchasing a like kind exchange (called a 1031, exchange).
If you used it as your primary residence,a nd it was a single family dwelling where no part of it was used as a rental income, then it would not be eligible for such an exchange.
However, NY taxes are based on the federal return. If this apartment is your primary residence,and report capital gains on scheduled D of the federal return, then you will include that gain on your New York return.
The botXXXXX XXXXXne, is the best you can do is to make sure you have capitured all eligible expenses to increase your cost basis.
The cost basis for mula is:
Adjusted cost basis= (riginal price + major repairs, improvements and additions, + any closing costs from the original purchase not already taken as a deduction else where ) - the cost of selling.
cost of selling includes such things as: advertising, mileage, realtro fees, etc.