Planning school visits -or- How many schools in 1 week?

If you are just looking to visit the campus, then like everyone said - it's doable, but not advisable. The whole purpose of visiting schools is that one gets to learn more about the school culture first hand. The campuses would be mostly dead in July, with FYs out for their internships. I was in your shoes last year, and chose to visit later in September so that I could interview at a few campuses and get a better understanding of the vibe at each school. Also, that way I had much more to write (essays) and speak (interviews) about what I liked about each school. Not to mention, you would meet some cool people who could guide you really well.

Having said that, if you can't make it in Sept./Oct., do visit in July.

Appreciate all your feedback!

Kanes, you're asking me a very good question, as to what I plan on doing while on campus.
I will try to schedule it in a way that I get to join at least a few information sessions, such as Harvard's and ideally Booth's.
Besides that I'd walk all over campus to get a feeling for it, whether I'd be happy spending most of my time for two years on site.

It really is a bummer if there's absolutely no students during the summer months but I won't have time in September/October due to the R1 dead lines. Visits in October for R2 deadlines would make sense, but then again I need to apply to some schools during R1 first and flying to the States twice is going to be rather expensive.

What else is there to do on campus during summer? I've tried the search function but most school visit posts are about class visits and student representatives showing one around during non-summer months.

Booth & Kellogg
Google Maps displays a distance of 22 miles / 41min driving.
Booth has got info sessions followed by campus tours Mondays & Fridays from 10:30am - 11:30am.
Kellogg has their info sessions on Mondays & Fridays starting at 2:00pm.
I believe I could manage both schools on one day, arriving at Booth earlier to have some 'private time' and staying at Kellogg longer after the info session is over.

Harvard & MIT
They all seem to love Mondays & Fridays
Sessions at both schools available on 11/July, HBS begins at 1:15pm, MIT hasn't announced the time on their website yet.

Columbia & NYU
As AjMBA noted, they're just a subway ride apart.
Both have sessions on 8/July and 10/July.
CBS sessions begin at 1:30pm or 1:45pm, NYU sessions begin at 4:00pm.

Columbia has MBA Info sessions on Mondays and Student Chats on Thursdays.
According to their calendar these student chats also take place during the summer, which is great!

I plan to spend an extra day in Chicago to spend a little time in the City and another two days in New York, to see a little and meet some friends, now that I'll have finally had the chance to fly over there.

The only school in such agenda, which I'm missing, is Yale.

NYU to Columbia is easy. If you aren't making a class visit then you can ride the ( I think A train) from downtown to uptown in about 35 minutes. The train lets you off right on Columbia's campus and you can walk around campus. NYU is much more scattered around so there isn't really a campus to walk but you can find the specific building I guess. Overall if you aren't visiting a class I don't see why you couldn't do both NYU and Columbia in 5 hours total.

If it were me and I was trying to maximize a visit to the US (you are coming from China?) I would go NYC (Columbia & NYU) > Boston (MIT & Harvard) > Chicago (Booth & Kellogg). I would skip Yale due to inconvenience. Yale is about 2.5 hours by train to NYC and Yale campus is about a 20 minute walk to the train station and you would probably want to go back to NYC instead of staying in New Haven.

Cornell (not on your list but maybe your interested) is a 5 hour bus ride from NYC and cost about $50 for a one way bus ticket. From Cornell (in Ithaca) you could probably fly to Boston from the Thompkin airport. The Thompkins airport in Ithaca definitely flies to Philadelphia which means you could add Cornell and UPenn if you were gutsy

I drafted a preliminary schedule earlier today:

Thursday: Arrive in the States
Friday: Visit both, Chicago & Kellogg
Monday: Visit both, HBS and MIT
Tuesday: Visit both, CBS and NYU

It sucks that the school visits are squeezed into three days but their info sessions are on those days so I assume it's better than walking around all by myself.
It will also leave me a few days to do some sightseeing in Chicago, Boston, and New York City.

Read several posts that the dress code should be forma, in a suit.
Does this also apply to visits during summer, with rising temperatures and deserted campuses?
Or would smart casual suffice, e.g. nice pants with a shirt, and possibly a light sports jacket?

If you're not going there for an interview I feel that business casual is sufficient. Your "smart casual" would work too. That's my opinion. I never visited a school in a suit(if I wasn't interviewing).

I visited all campus in khaki pants and a button down shirt - no tie. I was also sitting in on classes. I didn't feel out of place and other student visitors were dressed even more casual than I was. For information sessions there were people who showed up in shorts + Sandals (in California.. ). A suit is probably too much and shorts + Sandals are too little. Dress how you feel comfortable though.