I need a way to do the following...

 

plot 5000 unique addresses 

plot how many of those unique addresses fall within a given radius of 3 individual locations

 

 

what do I need to do this?

If you want it on a web page the google map API will allow you to do this.

this might work for you. If you have all the coordinates. It even has a way to upload the coordinates from a csv(excel) file.

 

http://www.freemaptools.com/radius-around-point.htm

i looked at google earth and google maps.. but I was really struggling to use it cleanly.. 

I had to plot storm drains and outfalls in large section of Holmdel as part of a non-point source pollution study at an old job I had. We captured the coordinates with corrected GPS locations and used a program called ARCView to plot them on a map. Worked pretty well and have the data you are asking for.