Hiya,
I went to Amsterdam 3 or 4 times. It has more than 2 squares though
I liked the Chinatown. They told us it's the oldest Chinatown in the world. It's across Central Station near the Zeedyk <sp?>. They have also a marihuana college and museum there lol. I found that hilarious!!!
There is the Dam, nearby the palace and across hotel Krasnapolski.
Rembrandplein and Leidscheplein have some cafés. You got a nice comedyclub there called Boom Boom Chicago. The shows are in English. We went to one of those and I found it pretty funny!!!
Museumplein is what I liked best. It's a nice walk from Leidscheplein and you can't miss out the Van Gogh museum. There's a nice park too. Vondelpark.
Melkweg is not a square. It's a venue. They have concerts there.
If you wanna go shopping stay away from the shopping-area nearby CS. It's boring. Only chains such as Zara, Footlocker and on. They got those anywhere in the world. Go shopping nearby Museumplein: PC Hooftstrat. That's where the cool boutiques are at.
For the good weed

I don't know the places. I didn't go to those. I was pregnant of my son at the time hehehehe
Just one thing: Be prepared of the rudeness. Dutch people are pretty rude. They don't stand in line for the train or bus, they are always in your way, they will bump into you and curse at you lol and on.