What I want is to find a cheap 3 bedroom duplex and buy it outright.

I was able to get the property relatively cheap because of the tenant situation.

To replace the system is expensive, the test isn't cheap either but knowing the state of the system is important. 

So you have to find a property that is likely not so nice, and buy it for a "AS-IS" price, then make improvements and enjoy the reward.Curb appeal drives rental pricing; If an neighborhood rents for $1,400 normally, and you find a rundown home renting for $950. 9 out of 10 times, its renting cheap because the LL wont improve the property, and likely has non performing tenants in it... so you buy at a cashflow price on the $950 minus repairs, then rehab and rent it for $1,400.

You do not need many responses to be successful but this is a difficult game to win on the cheap.

I think being in NYC, if you can buy the lot for cheap and have the connects to build a home, there is incredible value there.

Loaning a on most likely cheap non warrantable condo is a lousy loan to make.

I would like to invest in multi family but around here good multi families aren't cheap.

Since it was in the middle of recession (end of 2009 - beginning of 2010) I got the property very cheap, for 125k.

One other idea, that might show the tenant you're as concerned as he/she is, is to put up a fairly cheap surveillance system to monitor and entrance where the packages might be dropped off during the day.