Welcome to Radio Reference, and the great hobby of aircraft communications!
If you ever though Public Safety was hard to get..... think again!
I think we can all agree that aviation is the hardest thing to get, in basic terms.
First of all, I am assuming you are using the default antenna with your scanner, correct? If so, this will be the first thing you need to fix. Aviation radios run on very low power, so unless they are close, you won't hear anything. Same goes for ATC, they only put out roughly 10-55 watts of power, so they are quite a trick to getting.
If you don't have a outdoor antenna, I would recommend the ST-2. It is a very great antenna for the money, and it does quite well on the air band for it's price. It comes with all you need to get it going, 50' of RG-6, and a BNC connector. It is also good for other types of scanning if you do Public Safety or HAM bands.
At airports, they don't really have very high towers at all, around 50' or so. The reason for that is because the aircraft are high enough that their is no obstacles to get in the way, unlike Public Safety, etc. Since the such low wattage, and low height, the air band ATC side is very hard to relieve on the ground.
So yes, it isn't much of a thing of how close, just you need a good antenna! I can sit in my house and listen to the FD/PD, but can't think about picking up the AWOS, although the airport is 7 miles away. So my recommendation is that you get a outdoor antenna. Mount that sucker as high as you can. The higher, the better. You can never have to high of an antenna

If you are very serious about it, you will want to get one of the DPD Productions Log Periodics, and you will really be going then. But, living 20 miles away from the airport, you should be fine with a ST-2.
Aviation is strongly simplex. There are no repeaters that you input in, and output in. Everything is on AM, which makes DX'ing fun on the air band during ducting, I have logged planes in Savannah Georgia, about 150+ miles away on ACARS, and ATIS's 100 miles away. So their is no rif-raf about trunking, CTCSS's, repeaters and all of that crap! Just a frequency and your'e in business. Therefore, the new scanner won't help.
Also, I am not sure what you are using for frequencies, but here is some to get you started (Try
AirNav ):
COMMUNICATIONS - CTAF - 118.575 UNICOM - 122.95 ATIS - 133.8 REMARKS:
C914-948-0130. Dep. ASOS - REMARKS: C914-288-0216. NEW YORK APP - (R) (E) 120.8
124.65 126.4 257.65 REMARKS: (126.4 Opr 1200-0400Z++.) (120.8 Opr
0400-1200Z++.)(TRSA) TWR - Opr 1100-0400Z++. (E) 118.575 381.2 GND - 121.825
284.65 NEW YORK DEP - (R) (E) 120.55 257.65 CLNC DEL - 127.25
If you have any questions, ask!