I have a lot of best moments (and this is very incomplete because I didn't even try to go through all of the arcs in S4)
No Trip scenes
Strange New World: Archer having his picture taken with T'Pol.
Sleeping Dogs: T'Pol teaching Hoshi how to calm herself.
Minefield: Great character scenes for Malcolm: Behaving like he's facing a firing squad just before entering the captain's mess. And breakfast.
Damage: Archer is going to take the aliens' warp core and meeting with Phlox about the potential for casualties.
E2: T'Pold's meeting with Archer.
Azati Prime: I really loved Archer's last words to the crew before taking on the suicide mission.
Trip scenes
Unexpected: Trip and Ahlen in the "ice cube scene," contrasts with T'Pol's reaction in sickbay to the pregnancy.
Shuttlepod One: Trip blowing out the "candle" to save a few minutes of oxygen after Malcolm's admission about never being close to people before his posting to Enterprise.
Desert Crossing: Archer and Trip stripping off their shirts. Favorite: Archer tends to Trip in the shelter. He's so gentle - this is the captain I wish we had all the time.
Two Days and Two Nights: Trip and Malcolm's reaction to the transformation of the "muggers."
Singularity: The whole episode is golden; my favorite is Archer reading his perface to Trip who is paying absolutely no attention and then they two "discussing" it afterward.
Stigma: Trip awkwardly trying to tell Phlox his wife has been hitting on him.
Cease Fire: The goofy Cap'n Trip of "The Seventh" infamy is left far behind to be replaced by the self-assured and competent Capt. Tucker who risks the ship the prevent war.
The Expanse: The opening teaser. And Enterprise in orbit, the crew surveying the destruction, except for Trip, who can't look.
Similitude: Absolutely love the whole episode, but my favorite scenes are Sim telling T'Pol his/Trip's feelings for her; Sim and Archer in Trip's quarters; and Sim telling Phlox he was a good father.
Proving Ground: Trip talking with Shran, asking for help and getting it. God, I love that Andorian!
Harbinger: Who's attracted to who?
The Forgotten: Trip's breakdown.
The Council: The murder of Degra.
Zero Hour: Archer takes out Dolim.
Home: Trip and T'Les just before the ceremony.
Cold Station 12/The Augments: Archer trapped was a great cliffhanger and then his escape was really cool.
Observer Effect: Archer handing over command to T'Pol and then looking after Trip as he dies.
In a Mirror Darkly: Tucker is in the booth and Archer orders Reed to "break him!" Chilling.
Terra Prime: Archer's speech (boy, did they get this one right!); and the final scene with Trip and T'Pol. What a beautiful finale.