After thinking over it for a bit, here are some ideas that I want to try in TFA:

Cut Finn seeing the death of his stormtrooper friend. It introduces a weird subplot with humanized stormtroopers that’s never really continued throughout the rest of the trilogy, and Poe killing Finn’s best friend makes their relationship afterwards feel really awkward.
Cut Kylo freaking out when he hears about Finn and Rey for the first time. It’s a pointless comic relief scene that makes Kylo feel like a joke, and it implies a past between Rey and Kylo that was never really expounded upon.
Cut the whole deal with the Rahtars and Kanjiklub. It adds nothing to the movie, and just drags the pace down. Because of this, Kylo’s first conversation with Snoke has been postponed to after the heroes are spotted in Maz’s cantina, and the scene with Vader’s helmet that was originally there has been postponed a scene later.
Starkiller Base still destroys the New Republic in that scene’s theatrical place, but the reaction shots of the heroes observing it are gone. It completely destroys any sense of internal consistency with how far apart things are from each other.
Cut Kylo freaking out when he realizes Rey escaped, for the same reason I cut his earlier freakout moment.
The First Order no longer discovers the Resistance base’s location in this movie. It was always a lame attempt to add tension to the final act, and removing it helps the time skip between TFA and TLJ feel more believable.
Like I said already, Artoo doesn’t give the map to the Resistance, leading to Rey going on a one year search to find Luke. The credits roll after the Falcon jumps to hyperspace.