“我正在看这个城市”Remember, in Chinese, we normally put the "我" at the beginning of the sentence when you intend to say something related to yourself. And about the word"experiencing"， I think it's better to use another saying "感受" than"看". ' 看' is indicating the state of looking at an object or something else, "感受" is a bit more focusing on the feeling when you look at the city or objects. Actually “经历" , the experience or say the feeling is based on looking . I hope it would be helpful . Wish you happy studies with Chinese! :)

我正体验这座城市

正在means v+ing,but过means v+ed,so正在and过can't use at the same time.I am experiencing this city now：我正在游览这个城市.Can you understand me?

I am experiencing this city now in chinese, we will say " 我正在体验着这座城市”“我正在体会着这座城市”“我正在经历着这座城市”“我正在感觉着这座城市" these sensteces are popular in chinese you used to express , you are in this city, learn history, culture, language or something else, tour this city about the building, street, sights,etc. you just want to feel this city as much as the native people Amy

You could say 我正在体会这座城市. ：）