I'm dizzy from reading this play where each scene moves to a different location all around the Mediterranean, and where the personal and the political swirl together more confusingly than the current political scene in France. (Parallel in the news: the loser of the recent election, Segolene Royal, has dismissed her lover and rival for political leadership of the French socialists. Bedfellows make strange politics there. They will soon be forgotten in France, and have hardly been noticed at all over here.)
In movies, there are often examples of swirls like this. By chance, in the midst of my reading the play, we watched the film Babel, which jumps between Africa, Japan, San Diego, and Mexico with alarming jumpiness, and a lot less skill than Shakespeare. (I didn't like the film much and wouldn't even mention it except for the coincident jumping.)
Shakespeare usually has a more coherent focus. At least I usually find it a lot easier to follow the action and thematic development of a play. Here, he includes many descriptions of the exotic locales. Maybe he would have been pleased to have the filmmaker's choice of showing the many settings visually, but the richness of the descriptions suggest that he loved doing it the way he did.
As I say, I feel somewhat lost in the plotting. Anthony has much to lose, and he loses it: his political power, his family connections, his military might and reputation, and his relationship with Cleopatra. She of course is suggested to be older than most women in their prime, but to have an inexhaustible prime to call on.
I could start pulling up all the utterly famous quotes that set the exotic scenes, create the amazing character of Cleopatra, and cause one to share the depths to which Anthony falls. But I don't feel the need to do what's been done so often.
Bevington's Wide and Universal Theater demonstrates that every age had a new way to visualize and present Shakespeare, and that the 19th century was especially prone to make every word into a concrete onstage image, while 20th century performances sometimes are more abstract than the original productions at Shakespeare's Globe. Here's an image I found that really goes over the top, painted by Alma-Tadena in 1883.