Re: The Nuclear Wizard cantrips question:
From the Warlock list, you can take any 2 of Prestidigitation, Minor Illusion, Mage Hand, or (if Orzhov) Guidance. All of these should be useful even when they're Cha-based.
From the Wizard list, you can pick up any of Create Bonfire, Shape Water, Control Flames, Mold Earth, Lightning Lure, Fire Bolt, Toll the Dead, Frostbite, or Thunderclap. I recommend having at least 2 offensive cantrips for the Nuclear Wizard. Other than that it'd depend on my concept and party.
I elaborate on why I like each of these cantrips for the build in the Nuclear Wizard post itself, in a spoiler block near the bottom.
Re: The Hobgoblin Abjurer Offense question:
Unlike the Nuclear Wizard the Hobgoblin Abjurer doesn't really fundamentally change which spells are best on offense, so it's pretty much all of the old Wizard standbys. Cast Sleet Storm to lock down a mob and pitch Fireballs into the chaos to wipe them all out. Buff yourminionFighter and watch their DPR skyrocket with the right buff (which buff you should pick depends on their build more than yours). Raise an army of the undead and give them bows. Or throw down a pile of daggers and animate them with Animate Objects. Have your familiar Help people, or cast Dragon Breath on it, or whatever. Or don't even worry about damage and just focus on using stuff like Hypnotic Pattern or Wall of Force. You know, Wizard stuff. All kinds of options.
That's all I have time for right now, hope that helps!