Abstract: This study brings the results of comprehensive analysis aimed at finding the best tourist routes between twenty important tourism sites in Serbia: sixteen medieval monasteries at Fruška Gora Mountain, two other important monasteries in the area, and cities of Novi Sad and Belgrade as starting points of tours. Several travelling salesman problems are formulated and the shortest tours are found with the application of heuristic approach and genetic algorithm developed specially for this purpose. The best tour connecting all twenty sites of great tourist interest is firstly identified in strictly geographical terms by using GPS coordinates and orthodromic distances. This result, considered as the optimal in mathematical sense is not achievable in real circumstances, but can serve as target and be compared with any other solution obtained as if the touring all sites is made by car. In this study the distances between sites are based on node-to-node ground transportation infrastructure data downloaded from the Google Maps Service at Internet. Shortest tours respect topography of the area and can be used for planning tourist and other visits to monasteries and cities of national and international importance. The results of this study are considered as input to improvement of existing government policies affecting Serbian travel and tourism marketing. An approach is applicable elsewhere with open agenda for extensions and further improvements.