Sometimes I like to monitor my local towers, so I have this situation, too. The tower base stations are usually fairly low power. They have to reuse those frequencies at other airports, otherwise they'd go a very far distance at altitude, so they are pretty limited. The antennas are also usually unity gain.
All that, coupled with your scanner's sensitivity and antenna would mean that you'd hear the aircraft fine, but you'd only hear the tower if you were close by (or up in the air, where most of the signal is trying to go). My office is about 2 miles from the airport and I can barely hear the tower with an HT. I need to put it by the window to hear anything. The aircraft come in great if they're in the air. I can't hear them at all if they're on the ground. I can't hear the further airport at all from the office and would need to either be at the airport or at home.
If you can have an outside antenna - a quarter wave would be fine - get it up as high as you can, use cable that's got lower loss characteristics and I'd bet you would start hearing the tower.
Good luck and good listening!
There are several frequencies that are used at airports. If it is an airport like PHL, PNE, JFK and so on they have 1 or 2 frequencies to control aircraft landing and taking off from the airport. This is call the "Local Control" frequency AKA tower frequency. These transmitters are all 10 watts. the antennas are any where from 15' to 40' off of the ground for the most part. They are not reused in the same general vicinity where several airports are located. For example one of the tower frequencies at PHL is 118.5 MHz. the next closest FAA facilities are in Niagara Falls, NY, Norfolk, VA, Bedford, MA and Cleveland, OH.
The other common frequency used at airports is called ground control. A common frequency is 121.900 MHz. In recent changes the power output of many of these ground control transmitters has been lowered to 2.5 watts. This is due to RFI between closely located airports, about 60 miles separation.
Here where I work at the FAA Tech Center the Atlantic City airport ground control is on 121.900 MHz. So is PHL, Baltimore, Md and 40 other facilities in the northeast. Ground control is engineered to be used for a radius of about 2 miles around the transmitter/receiver.
At other uncontrolled airports you have frequencies called unicom or airport advisory frequencies. these are on a frequency like 122.800 MHz. These frequencies will be used in the general vicinity of several airports within about 1 - 20 or more miles of each other.
So it depends on how the frequencies will be used as to how close two facilities will use the same frequency.