It depends on what your plans are when you get there. Are you going for culture or just to lay on the beach? I don't think others can make up your mind to what you want to do. All I would add is if you haven't been to one but to the others go someplace new.

I think I would have to choose Italy

Here are areas I'd like to visit.
Sistine Chapel
St. Peter's Basilica
Bridge of Gold (most all the shops on the bridge are goldsmiths)
And I'd love to take Gondola rides in the evening after devouring authentic Italian cuisine!

It really does depend on what you are going for. But at all three destinations it will be very busy, and crowded, as Mid July to end of August is the peak of the tourist season. First of all it depends if you are going to visit a lot of musuems and want to spend a lot of time in the cities. Italy has so much to offer, but keep in mind, things are really expensive in Italy, food hotels, etc. Montenegro has stunning scenery, and is a lot cheaper than either Greece or Italy. There are lots of interesting old things to visit in Montenegro, and the beaches are lovely, but keep in mind, they are mainly pebble beaches. The Greek Islands are great, but Athens has wonderful history, but is also more expensive than some of the smaller Islands. Also keep in mind, this is the hottest time of year as well, so be prepared for heat and crowds! Hope you have a lovely holiday, whichever you choose.

It depends! I don't know much about Montenegro, but here are the selling points I know of for Greece and Italy. You should pick what you like! Also note that both places have warm weather, beautiful views, beaches, wine, and a hopping night life.

Greece
Seat of Ancient History
Home of Aristotle, Plato, and Socrates--seat of the origins of modern philosophy--ancient ruins survive and can be toured and photographed. Ancient artwork and craftwork survives and can be seen in museums.
Home of Sparta, the setting for the movie 300
Home of Greek Mythology, which you probably studied in school. Actual ruins show you that these were not just stories to the people. They built monuments to these gods.
Site of much that happens in the Bible, you can take tours of where Biblical things happened
Gyros

Italy
Birthplace of the Renaissance, when the philosophical method of Ancient History was reborn
Home of Michelangelo, who sculpted the Bible's King David in the nude--you can see it!
Home of Venice, the sinking city built around a hundred tiny islands with a system of canals
Rome and the Romans and the Holy Roman Catholic Church and the Pope--a triple ton of history is documented here in museums.
Verona is here, the setting of Romeo and Juliet
Ravioli, Espresso