As you are aware since your vehicle's registration is currently suspended, if you do not have insurance coverage and you do not surrender your vehicle plates to the New York DMV, your registration and driver license are suspended indefinitely.

If you had a lapse in your insurance coverage in New York State and did not surrender your vehicle plates immediately, your registration is suspended for the same number of days that you did not have insurance coverage, but did hold the vehicle plates. If the time is more than 90 days, your driver license is also suspended for the same number of days as the registration. To reinstate your driver license, you must pay a termination fee of $25 when the suspension ends.

The New York State Department of Motor Vehicles site lists the civil penalties amounts for registration suspensions due to an insurance lapse. As for your parking situation, you may need to find a private parking lot or storage facility that will allow you to park your unregistered car until you are able to get the plates back on and your registration reinstated since most public lots, such as your apartment's lot, will tow your vehicle if it is without current registration.

You will need to contact the NYS DMV to find out if there is any temporary parking registration or other type of decal you could place on your car in its current location so that it will not be towed. 

If you still need to place insurance on the vehicle in order to get your registration reinstated, click here for a free auto insurance quote.