The paper describes computational experience comparing the methods of Elzinga-Hearn and Megiddo for the smallest covering circle in the plane, the conclusion being that the first remains much faster even for 1000 points. Before asking about tools it is more important to determine exactly what type of problem you are facing, and to choose an adequate model. Only then can one talk about solving and with which optimization methods. If you are interested in theoretical work and research then I can say that location models touch upon many fields. Unfortunately most material is only found in print and not directly accessible electronically.
Primary information is the following.
Also many algorithms exists aimed at generating these sites in an efficient way. Most of such models are rather in the continuous area.