Here are the character's types according to my own analysis:
Carrie Bradshaw is a 6w7 and also an ENFP. She's very warm, concerned for and loyal to her friends but also a bit jumpy and nervous. There is a palpable anxiety about her - she's always asking questions and fretting about her love life and her social theories. Carrie is also funny in a somewhat self-deprecating way and tends to appear as unsure of herself and clumsy, but also intellectually witty and surpsingly insightful. She's always consulting her friends before she makes most decisions and has issues on dependency/independency matters - needs a lot of support but doesn't want to be suffocated (has panic attacks over marriage but still clings to the relationships). Her love for expensive shoes, fancy restaurants and clubs indicate a strong 7 wing.
Samantha Jones is a 7w8 and an ESTP. She's mainly interested in having fun and entertains herself with her own sexuality and excessive explorations of it. She tends to overdo things (and men) and is a complete epicurean and hedonist, ignoring and dismissing the painful side of life and love and focusing solely on the pleasure that she's after. Samantha loves variety and change and is afraid of losing her freedom by settling with a safer lifestyle. She's also concerned with power issues (the 8 wing), but she's willing to give up a bit of her power in order to obtain more enjoyment.
Miranda Hobbes is 1w2 and INTJ. She mostly denies her feelings and softer side, but it's obvious to everyone else but her that she has them. She's very orderly and rigorous, a devoted rule-follower and a reliable friend and employee. Very concerned with her own principles, she becomes quite inflexible and has trouble with giving in to her instincts and wilder side. Her repressed anger also adds to her tension and rigity, making it difficult for her to empathise and accept other viewpoints. She's skeptical and cynical but ultimately also an idealist, finally learning to help people and give them direction and unconditional love.
Charlotte York is a tougher one to type. For now I'd go with 3w2 and ESFJ. She's driven to achieve the perfect love and the perfect marriage and is completely focused on superficial values like a man's financial situation and social prestige. She atracts by trying to figure out what men would value in a woman in order to want marriage with her and acts that way, while at the same time ignores and dismisses her own feelings in the process. Although mainly concerned with the perfect love, she lacks in altruism and is actually very selfish and goal-oriented. She's very concerned with image and wants to appear refined, respectable and feminine - in other words perfect for marriage with a perfect man. In the end Charlotte manages to psychologically evolve - she looks behind the appearances and falls in love with someone that can satisfy her deeper needs.
Mr.Big is a 9 with balanced wings and probably INTP. He won't seriously involve himself in anything and is generally concerned with comfort and maintaining a balanced, easy-going detachment. Has a calm powerful presence - he's hard not to notice. He also loves the good life and the lack of responsibility. Disengaged, peaceful, unconcerned and somewehat adventurous and unpredictable.
Aidan Shaw is a 9w1 and ISFP. Relaxed, pleasant, a bit boring and plain. However he does have a self-righteous streak and a certain rigidity about him. Seems open and flexible but he's really fairly stubborn and intolerant.
Trey McDougal is probably a 9w1 and ISTJ. Lacks in personality and is overly submissive to his mother's overwhelming presence.
Aleksandr Petrovsky is probably 3w4 and INTJ. He has a colder, self-centered, career-oriented personality and tends to appear as refined, sensitive and special at first sight. He's very concerned with other people's opinion of his work and aims to impress Carrie by showing her a romantic side that doesn't truly characterize him. Once he obtains social validation, he forgets about her.
Steve Brady is a 9w8 and a ESFP. He's optimistic, trusting, easy to get along with and overall a nice guy. He's unstructured and relaxed, with relatively low expectations out of life. Accepting and tolerant, at times he will tend to emotionally react to events and is not as calm and undisturbed as the other 9s in the show (8 wing).
Harry Goldenblatt is probably a 9w8 and ENTP. Also accepting and tolerant, playful and understanding. A nice guy. Is relaxed and supportive, while at times can boldly go for what he wants (wing 8).
Smith Jerrod is most likely a 9w8 as well and an ISFP. Samantha directs him and he's there for the ride - he's a bit disengaged with his career and whatever else is going on in his life, apart from his relationship with Samantha of course. He's accepting and nice and doesn't mind that other people decide for him, but he will be there for his girlfriend in a more assertive way.
Stanford Blatch is probably a 9w1 and INFP. Relaxed, accepting, sweet, almost never takes offense over anything and is a pleasant individual alltogether. Is a warm friend and has a knack for colorful flowery clothes. Can get rigid and intolerant at times (he dumped his boyfriend because he used to be an escort in the past), but generally he will be optimistic and forgiving.