I don't know how this conversation turned to NFL.  The original post didn't mention NFL at all.  That being said, I can check to see if NFL recordings on broadcast OTA tv will allow you to watch recorded video on a delay.  I have a antenna feeding into an AirTV which I can use to watch the OTA stations within the SlingTV App (not Slingbox, SlingTV). The AirTV has a SD card slot to allow you to insert an SD card for DVR storage.  I can watch recorded content anywhere in the SlingTV App, or on a Roku (can throw a Roku Stick in a hotel TV perhaps, providing their wifi doesn't suck like most).

For non sports content, don't just about all major cable and sat carriers now have an app you can watch off site?  I know the local cable companies here and Dish Network do.