There are several types of ceiling lamps in the Georgetown. I have replaced all my interior lights with LED. The light fixture I think you are describing uses a T-10 or #194 push in style bulb. A typical one of these on ebay can be seen searching for auction # 170949343181 Other auction listings may have better pricing, this is just an example.
For this type, you want to get an LED bulb replacement that has a bridge rectifier (the small black square) on the back side of the LED circuit board. This makes the LED module polarity independent. LED modules without a bridge rectifier may need to have the light fixture wires reversed, as LEDs unlike light bulbs, are polarity dependent.
The other factors to consider are how many lumens (brightness) you want. This is determined by the number and size of individual LEDs installed on the circuit board. The remaining consideration is whether to purchase warm white (3500 degrees, more like a light bulb color), or bright white (6000 degrees, more bluish color).
Hope this helps