Hi and welcome. Pilot spouse here. We do tons of nonrev and he commutes CVG to NY base. Experience with JFK or LGA any given regular day:
start early, it can be hopeless after 2 pm or wait until late ones to JFK (too late for INTNL conx) but you'll have hotel expense. We use Five Town Motor Inn 516-371-2600s w/free shuttle out of LGA or JFK. If you need car between airports, we use Kew 718-846-6666
My husband starts his commute early or night before. Much of OUR service is not DL, tho.
It's really hard to do some days even with 23 yrs on an S3. I guess you're S3CR?
You may fare better out of ATL these days

We find it's easier for INTL travel and I always get business class. You have the NW option now, via DTW, too. Domestic just gets so iffy--several times I have not made an overseas trip due to domestic flight problems. Oh well...
Happy to offer any more tips--I'm sure you'll get lots of advice from some our intrepid flyin' fools!