Removing the roll to Hit is something thats been covered before but what would you add to make it interesting on a per character basis, Ability Checks? Like a Dex save to reduce damage dealt to HP? And how would you handle Conditions that normally would grant adavntage/disadvantage?
Removing a roll then having to add another roll "to make it interesting" doesn't sound like a great plan to me.
If you want to remove randomness in attacks, I'd use averages i.e. as if a result of 10 was rolled, which is the same as what you do with passive checks. Advantage and disadvantage would be the usual +5/-5 as in passive checks. Then you can either keep the damage randomness, or remove that one as well, like per the option already given for monsters in the MM.
If you want to retain randomness, but still prefer not to roll to hit, you can roll "defense" instead of using static AC, which in fact is calculated from a base value of 10. Replace that 10 with a d20 roll: a regular character would roll a defense of d20 + Dex modifier + armor bonus + shield bonus. The armor bonus is derived from the armor's AC in the PHB minus 10. So instead of rolling an attack against static AC, you roll defense against a static attack DC which is 10 plus all the usual attack bonuses.
I can imagine a group also using both options at the same time if the players like rolling dice as much as possible: PCs roll attacks vs static AC (as usual), and roll defense vs static attacks done against them.