Long Island is relatively flat. UHF comes in poorly, VHF is 50/50, some nights good some not good, 800mgz not all all. Got a couple of hits on my deck on the 800mgz. nothing to speak of.
So, something to consider....
Two way radio systems are designed for radio coverage in the area they are licensed for. Usually the license will say something like X km radius around point y. Point Y is usually the repeater site, or center of a multi site system. FCC and frequency coordinators do it this way to limit coverage to the necessary coverage area. This lets frequencies be reused by other agencies. Technically, the mobile and portable radios are only permitted to transmit inside the area where they are licensed.
Designing a radio system to cover its intended area takes some work. The antenna system design, RF power levels, etc. are all part of the equation. By using RF power levels and antenna design, a system designer can maximize coverage inside their operations area. The coverage outside the licensed area is sort of a bonus for scanner listeners.
Since the radio systems you want to listen to are probably designed for agencies outside your immediate area, it's going to take some effort to get the coverage you want.
As suggested, it would be a really good idea to take the radio with back of set antenna up on the roof, or where ever you are going to mount the antenna, and see if you can receive the agencies you are trying to listen to.
The back of set antenna is going to be a poor performer as it's nowhere near tuned to the frequency you want to listen to. But, it can tell you if there is something there to listen to.
Inside the house with the stock antenna you have a couple of things working against you:
1. You are low down, so your "radio horizon" is pretty close, probably a few miles.
2. Metallic building materials, copper pipe, house wiring, etc. can all block signals.
3. Local noise sources inside your house, like consumer electronics, can drown out the weak signals.
By getting the antenna outside and up high, you are addressing these issues.
The higher up you can get your antenna, the farther it can "see". Since the frequencies you want to listen to are (for the most part) line of site, the farther your antenna see the more it's going to pick up, even stuff you cannot hear inside the house.
Getting the antenna outside in the clear gets you away from foil backed house insulation, vapor barriers, metal lath in plaster walls, wiring and plumbing. Some roofing materials can be metal also, so even installing in the attic isn't always going to work.
Taking the radio on the roof will tell you and us a lot.
If you can pick up what you need from there, mounting a suitable antenna on the roof, preferably on a pole, fed with good coaxial cable and properly grounded is likely going to be what you need.
In fact, you might be very surprised what you can pick up with a good outdoor antenna.
Key is, picking the right antenna, installing it correctly and using suitable coaxial cable to get the signal down to your radio with the minimal amount of signal loss.
There's some math involved here that can help figure this out, but we need to know if the signal is there in the first place. From there we can figure antenna gain, feed line loss, etc. to help you figure out the right parts list to do what you need.
One option that hasn't been mentioned is that you can get an old outdoor TV antenna and turn it sideways and mount it on the roof. The old TV frequencies covered portions of VHF, UHF and 700-800MHz. Old TV antennas were often a combined log periodic. You can find them cheap, and they'll work quite well. Also, you can use the standard RG-6 tv/cable/satellite TV coaxial cable to connect it to your antenna.