Sorry I'm late to this thread, but I saw the title and wanted to chime in about my own experience with an Eldritch Blast-free Warlock.
I called it the FrostLock.
Essentially: I wanted to be a Fiend pact warlock, but I wanted a different fiend. I was bored with the traditional "flames of hell" option and wanted to be all about frost and ice and Levistus instead. So I rolled up a White Dragonborn warlock, and I asked my DM if I could use the Ray of Frost cantrip in place of Eldritch Blast. She agreed, but only if it were a total replacement.
This meant that Ray of Frost would replace Eldritch Blast on my character's spell list, and invocations like Agonizing Blast, Eldritch Spear, Grasp of Hadar, etc., would all apply to Ray of Frost (only) for my character. I wouldn't be able to go back and also select Eldritch Blast. I know that sounds a bit harsh--everyone knows that Eldritch Blast is the best cantrip in the game--but honestly, I was so bored with that particular cantrip that I didn't flinch. Suboptimal choices don't really bother me.
So how did it go?
Well, adding my Charisma bonus to any combat cantrip is going to be good. Agonizing Blast is always going to be the warlock's first choice of invocation.
As with any warlock, your spells are your "build." My favorite spells with this character were:
- Toll the Dead, because I love this cantrip
- Armor of Agathys for defense (and thematic reasons)
- Investiture of Ice (arcanum)
- Misty Step for escaping grapples, breaking into shops through their windows, and getting out of tough situations
- Counterspell because it's the best spell in the game
- Hunger of Hadar for even more battlefield control
I picked up Elemental Adept at 4th level. I know this isn't a very popular choice, but I never regretted it. If your primary spell deals elemental damage, and your spellcasting ability score is maxed out, I highly recommend giving this feat a try.
My warlock was all about battlefield control: there's some really good synergy with Lance of Lethargy and Repelling Blast. On a good round, I could slow a singular target's movement by 20 feet, and also push it back another 10 feet...so unless their movement rate was greater than 30' per round or their AC was really high, it was never going to get close. And even if it did, I had options.
Tomb of Levistus was better than I expected. I chose that invocation purely for flavor reasons, but it really saved my bacon in the very next adventure, when a couple of heavy-hitting monsters managed to get into melee range. They tried to pummel me with Multiattack, but only the first of their attacks could penetrate my fortress of ice.
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Anyway. Sorry if it was off-topic, but that was my EB-free warlock character.