The time between commissioning and first reporting varies. For example, someone going to an airborne unit who has not been to airborne school may have an earlier BOLC date so they can get airborne school done as well. For those going Infantry, Ranger school is pretty much a requirement. In the past some LTs go to Ranger school prior to BOLC, some after. This may impact as well.
Class rank can have an impact. I know one Cadet who got her branch choice of Aviation but will not start flight school until April. No, she will NOT be off until April.
Many new LTs get details over the summer. West Point graduates will often help at West Point with Beast, ROTC graduates may help with "Advanced Camp".
If there is a longer break you may find yourself "snowbirding", or doing officer detail work somewhere. Maybe helping someone with a study. If you're in the right place at the right time you might even stumble into a short course. I was "snowbirding" (poking my eyes out in boredom) as an LT at Fort Rucker in a battalion HQ when I answered the phone. "This is captain _________, S-1, do you or anyone else there want to go to AGOS?" Me- "What's that sir?" Captain- "Air Ground Operations School. A three week Air Force course down near Destin. Do you want to go? We have to fill a slot." I looked at the phone, looked around the office... was this a practical joke? So off I went to Hurlburt Field (Destin Florida), for a 3 week Air Force course.
My brother, a USNA grad, had a long break before flight school. He was sent to San Diego for several months and hung out with a squadron there. Well, he hung out.
Leave has already been discussed. Understand that you usually won't just be able to take leave any time you want. Just as in the corporate world, there are busy times when "all hands are on deck".
You will also get passes from time to time for 3-4 day weekends. There are normally travel distances involved with these so don't plan on driving from say, Fort Stewart, Georgia to Colorado on a pass. These don’t count as leave.