Did you try to repair the rights of the files and folders of your computer and did you delete preferences?
Thank you Willi Adelberger ... Yes, I have done a "Repair Disk Permissions" twice and I have "trashed" my preference files more than the number of fingers on my hand. (But that of course leaves to thumbs!)
Please bare-this-in-mind, my problematic crashes started with the last InDesign update.
What happens, if you open InDesign and close it without working?
Did you trash Saved Data? As this causes often crashes.
What does the crash report tell?
Again, thank you Willi Adelberger ... I have completed a total "uninstall"; then a complete "re-install" with no "Sync Settings": open app, then close (just like before) ... crashes on close.
I am providing a quick "crash report"; this may trigger a new response for a solution:
* * * * *
InDesign quit unexpectedly.
Problem Details and System Configuration:
Process: Adobe InDesign CC 2014 
Path: /Applications/Adobe InDesign CC 2014/Adobe InDesign CC 2014.app/Contents/MacOS/Adobe InDesign CC 2014
Version: 10.2.0.69 (10200)
Code Type: X86-64 (Native)
Parent Process: ??? 
Responsible: Adobe InDesign CC 2014 
User ID: 501
Date/Time: 2015-03-05 00:09:36.427 -0700
OS Version: Mac OS X 10.10.2 (14C109)
Report Version: 11
Anonymous UUID: 3CED763A-0D93-6D0C-A090-63FC7A93BC31
Time Awake Since Boot: 34000 seconds
Crashed Thread: 0 Main Thread Dispatch queue: com.apple.main-thread
Exception Type: EXC_BAD_ACCESS (SIGSEGV)
Exception Codes: KERN_INVALID_ADDRESS at 0x0000000000000008
VM Regions Near 0x8:
__TEXT 000000010e37e000-000000010e384000 [ 24K] r-x/rwx SM=COW /Applications/Adobe InDesign CC 2014/Adobe InDesign CC 2014.app/Contents/MacOS/Adobe InDesign CC 2014
put the whole crash report on pastebin.com and give us a link to it here.
Thank you P Spier. Following your instructions, I have pasted the entire "crash report" on pastebin.com. So with drums and horns blaring, here is the link to the crash report link ...
Sorry to say I don't see a smoking gun. Seems to be related to widgets...
Thank you P Spier. Uninstalled InDesign CC 2014, re-installed InDesign CC 2014, opened without third-party plugins, and with brand new preferences... it still crashes on close.
P Spier, for clarification, please describe for me what you mean by "widgets," and why you intuitively sense this! I don't think InDesign uses widgets, or is it possible your are refering to my system (Mac OS X 10.10.2)
InDesign does use widgets (all the little buttons are widgets), and I got that from reading the crash report. Here's a basic tutorial on interpreting crash reports: Guide to Interpreting InDesign Crash Reports | InDesignSecrets