Either Providence (TF Green airport) or Hartford are about the same drive time to New London - however, the entire drive on I95 (from Providence, Rhode Island) can be jammed and a mess depending on your arrival time. Both arrival airports (from Denver) are serviced by Southwest which will have the best fares. I'm not certain about a nonstop to Providence but I do know there are non stops from Denver to Hartford. When you come, you'll need to stay another day and go to Mystic Seaport which is very close to New London. The last NRG Conference was in Mystic in the fall.
Hope to see you there! Safe travels...