Stayed at Bellagio twice and it is a little more upscale (IMHO). Saw tons of PWP (Prade Wearing People)...think hip and trendy! I was there for a conference so wore my basic black pant suits during the day and changed my top at night. I like to dress up a little so I wore my embellished sweaters and tops at night. I don't remember seeing people really dressed up (beaded gowns, etc.) except for at private functions. As far as restaurants go...it depends on where you decide to dine. If you go over to the Four Seasons and dine at Aureole...you'd feel out of place in casual attire and I believe a jacket for men is suggested. If you go to the buffet at the Bellagio...anything (well, almost anything) goes. If you aren't sure and are going to an upscale restaurant..call! Vegas like Orlando brings out every type of dress....even at Bellagio you'll see people wearing shorts and tanks and others dressed to the nines. Wear what is comfortable to you!
Weather is June varies but it starts to get hotter in the day. Bring comfortable shoes as ALL the casinos anymore are HUGE! Walking the strip can be a hike, too. I always bring a light sweater or two because they seem to keep places pretty cool there (especially at night).
If you have the time and inclination I highly recommend the spa (get a manicure, pedicure or massage) it was the best spa experience I've had! If you get a treatment you are allowed to use their facilities all day and they include whirlpools, steam and euclyptus rooms and all types of other facilities. Another thing we did was to rent a cabana. While this can be pricey for two...if you have a larger group, splitting the cost can make it affordable (I think it was about $150). It was great to have our own space while lounging around the pool. It came with TV, Tables, chairs and MISTERS and the waiters stopped by all day!
Bellagio is wonderful. Next to the Four Seasons, this is one of the stars of vegas as far as hotels go. The rooms are great, too. Expect to be impressed by the furnishings and the bathroom! I loved my stay there and I am sure you will, too. ENJOY!