Information on the Imperial Academy

Where is it located? Coruscant or Carida?

Neither.

Imperial Center doesn't have any mega-prestigious academies, really, save for the University of Coruscant. That one isn't one of the renowned Imperial Academies, but rather, just a high-level school. It used to be considered one of the best, until the Empire came around and kicked out all the qualified aliens for cultural reasons. When that happened, they had to replace the missing students, so they ended up replacing them with sycophants and COMPNOR SAGroup flunkies. As a result, the quality of the student body dramatically suffered and so did the reputation of the school. That damage even affects its reputation in the NR era, since people never forgot what happened.

Carida has an élite stormtrooper training camp--THE main training camp, actually. It's not an academic institution.

There are branches on Raithal, Prevsbelt IV, and Anaxes as far as I'm aware. There are certainly others: there's likely one in Corellia, since there was a reference to Mako Spince shooting the Academy's "mascot moon". Soontir Fel and Han Solo both attended this one.

Are the students allowed to have breaks and go visit friends and family? If so, for how long?

Absolutely. When you think of the Academy, think of a school like West Point or Annapolis. They definately have session breaks, and they are seasonal, like any university.

An important thing to remember is the Academy isn't solely for the officer corps or the military in general. It's also a very prestigious school system that can put you on the high track for any number of careers, including politics or civil service.

And are women allowed to enter the Academy? Are there any restrictions to getting in and are they treated with any kind of prejudice upon entrance?

In a word: yes.

Officially, all sentient Imperial species are treated equally and the Imperial Academies are a meritocratic system. The only restrictions in place may be the restrictions that the military places on women in real life as well.

I'd imagine it was coeducational, since females are certainly seen in large numbers in politics as well as civil service. There aren't so many in the military, but there are quite a few high level ones. We have to assume that females are a normal sight in the military, though, or Mara Jade couldn't possibly have successfully pretended to be a TIE pilot in Dark Force Rising--the people she was talking to would've noticed.

There wouldn't be any prejudice, since the evidence shows us that females are a normal sight in the military and civilian career areas. Indeed, we've only seen two examples of prejudice--one Daala, who is criminally incompetent and probably earned it, and one Illor, who likewise must've earned it. The majority of cases seem normal.

As with aliens, the only prejudice you might see would be from invididuals and not the academic instititution itself.