[Nexus One Android Development] woozyking:
I just encountered this issue and used an older Calendar APK and that seemed to solve the problem. The APK's mentioned from Texas ICS thread: http://xdaforums.com/showpost.php?p=21465864&postcount=1606

I've also got the logcat log, as attachment.

The key error I see should be in this range (but see the full log for details):

01-30 12:54:38.276 E/AndroidRuntime(18654): FATAL EXCEPTION: main
01-30 12:54:38.276 E/AndroidRuntime(18654): java.lang.IllegalArgumentException: column 'allowedAvailability' is invalid
01-30 12:54:38.276 E/AndroidRuntime(18654):	at android.database.DatabaseUtils.readExceptionFromParcel(DatabaseUtils.java:165)
01-30 12:54:38.276 E/AndroidRuntime(18654):	at android.database.DatabaseUtils.readExceptionFromParcel(DatabaseUtils.java:135)
01-30 12:54:38.276 E/AndroidRuntime(18654):	at android.content.ContentProviderProxy.insert(ContentProviderNative.java:415)
01-30 12:54:38.276 E/AndroidRuntime(18654):	at android.content.ContentResolver.insert(ContentResolver.java:735)
01-30 12:54:38.276 E/AndroidRuntime(18654):	at com.google.android.syncadapters.calendar.CalendarSyncAdapter.addDefaultCalendar(CalendarSyncAdapter.java:1203)
01-30 12:54:38.276 E/AndroidRuntime(18654):	at com.google.android.syncadapters.calendar.CalendarSyncAdapter.access$500(CalendarSyncAdapter.java:104)
01-30 12:54:38.276 E/AndroidRuntime(18654):	at com.google.android.syncadapters.calendar.CalendarSyncAdapter$2.run(CalendarSyncAdapter.java:1146)
01-30 12:54:38.276 E/AndroidRuntime(18654):	at android.accounts.AccountManager$Future2Task$1.run(AccountManager.java:1485)
01-30 12:54:38.276 E/AndroidRuntime(18654):	at android.os.Handler.handleCallback(Handler.java:605)
01-30 12:54:38.276 E/AndroidRuntime(18654):	at android.os.Handler.dispatchMessage(Handler.java:92)
01-30 12:54:38.276 E/AndroidRuntime(18654):	at android.os.Looper.loop(Looper.java:137)
01-30 12:54:38.276 E/AndroidRuntime(18654):	at android.app.ActivityThread.main(ActivityThread.java:4424)
01-30 12:54:38.276 E/AndroidRuntime(18654):	at java.lang.reflect.Method.invokeNative(Native Method)
01-30 12:54:38.276 E/AndroidRuntime(18654):	at java.lang.reflect.Method.invoke(Method.java:511)
01-30 12:54:38.276 E/AndroidRuntime(18654):	at com.android.internal.os.ZygoteInit$MethodAndArgsCaller.run(ZygoteInit.java:787)
01-30 12:54:38.276 E/AndroidRuntime(18654):	at com.android.internal.os.ZygoteInit.main(ZygoteInit.java:554)
01-30 12:54:38.276 E/AndroidRuntime(18654):	at dalvik.system.NativeStart.main(Native Method)
01-30 12:54:39.197 E/DatabaseUtils(5988): Writing exception to parcel
01-30 12:54:39.197 E/DatabaseUtils(5988): java.lang.IllegalArgumentException: column 'allowedAvailability' is invalid
01-30 12:54:39.197 E/DatabaseUtils(5988):	at android.database.DatabaseUtils$InsertHelper.getColumnIndex(DatabaseUtils.java:1077)
01-30 12:54:39.197 E/DatabaseUtils(5988):	at android.database.DatabaseUtils$InsertHelper.insertInternal(DatabaseUtils.java:1053)
01-30 12:54:39.197 E/DatabaseUtils(5988):	at android.database.DatabaseUtils$InsertHelper.insert(DatabaseUtils.java:1181)
01-30 12:54:39.197 E/DatabaseUtils(5988):	at com.android.providers.calendar.CalendarDatabaseHelper.calendarsInsert(CalendarDatabaseHelper.java:212)
01-30 12:54:39.197 E/DatabaseUtils(5988):	at com.android.providers.calendar.CalendarProvider2.insertInTransaction(CalendarProvider2.java:2116)
01-30 12:54:39.197 E/DatabaseUtils(5988):	at com.android.providers.calendar.SQLiteContentProvider.insert(SQLiteContentProvider.java:96)
01-30 12:54:39.197 E/DatabaseUtils(5988):	at android.content.ContentProvider$Transport.insert(ContentProvider.java:189)
01-30 12:54:39.197 E/DatabaseUtils(5988):	at android.content.ContentProviderNative.onTransact(ContentProviderNative.java:152)
01-30 12:54:39.197 E/DatabaseUtils(5988):	at android.os.Binder.execTransact(Binder.java:338)
01-30 12:54:39.197 E/DatabaseUtils(5988):	at dalvik.system.NativeStart.run(Native Method)