I am building a "lucky wizard" for my newest campaign.
The concept is to use abilities and features that allow me to reroll (or replace rolls) attacks, abilities, and/or saving throws (such as the Lucky feat). I'm not interested in abilities that allow rerolls on allies' or enemies' rolls.
My search so far has yielded a few options, but I am unsure if I've missed any.
Are there others?
There are a few ways to do this and I'm going to separate it into things that are available at level one, then go into options for later levels.
You've already named them: Be a Halfling (Lucky racial trait) or take the Lucky feat (variant human). Both of these options apply to Saving Throws, Ability Checks, and Attack Rolls (and the Lucky feat also applies to attacks against you).
Elven Accuracy allows you to reroll Dexterity, Intelligence, Wisdom, or Charisma based Attack Rolls when you already have advantage. Very situational, but an option.
And it's worth noting that if you didn't take the Lucky feat at as your Variant Human feat, you can take it later on.
With only two levels in Wizard, you can gain access to the Portent ability from the School of Divination (yes, I know you mentioned it, already). This isn't a proper reroll, but it replaces a roll with a value, which is spiritually similar. This gets an upgrade at level 14 to three uses.
Rogues have a handful of abilities that work similar to Portent, in that they allow you to set a static roll amount. Reliable Talent at level 11 makes your minimum roll a 10 for proficient Ability Checks; Stroke of Luck at level 20 allows you to auto hit or treat an Ability Check as a 20; The Swashbuckler subclass let's you reroll a missed attack, with advantage, no less.
Fighters gain access to Indomitable at level 9 (upgrades at levels 13 and 17), which allows them reroll failed Saving Throws.
Barbarian (Zealot) gains Fanatical Focus at level 6, which also allows rerolling a failed save. And Indomitable Might at level 18 replaces a roll lower than the Barbarian's Strength score.
Monk Diamond Soul (level 14) allows you to spend a ki point and reroll failed saving throws.
Wish can force a reroll of any roll made within the last round (including your last turn).
Glibness Allows you to replace any Charisma Check with a roll of 15. (Thanks, Patrick)
The Luck Blade allows one to reroll one attack roll, ability check, or saving throw, once per day. Sure, it's a legendary item, but it's an option.
Ring of Evasion (only a Rare item!) allows you to expend a charge to Succeed on a Dexterity Saving Throw that you had failed, as a reaction.
Dragon Masks (Legendary) allow you to succeed a failed saving throw once per day.
Clockwork Amulet is a common item that allows you to take forgo rolling an Attack Roll and instead use a ten, once per day. (thanks Tiggerous)
Some of the answers here are excellent in giving an inventory of things granting various kinds of players a reroll. But your question is "What abilities allow me to reroll?" And it's clear that "me" means a "lucky wizard."
So I am taking this to mean (a) we wan't to avoid things that would require significant multiclassing outside Wizard and (b) by "reroll" you mean to include gaining advantage on a d20, which can be seen as a kind of reroll (or equivalent).
Given all of that, you already listed three good ideas:
And others have pointed out these high-level spells:
Now let's look at what else could be of interest to a Wizard who wants to reroll frequently.
I would start with Elven Accuracy (From Xanathar's):
Whenever you have advantage on an attack roll using Dexterity, Intelligence, Wisdom, or Charisma, you can reroll one of the dice once.
This may seem situational unless, like many wizards, you are using a familiar to take the Help action to grant you advantage on attack (one might recommend an owl, for reasons explained in this answer).
Next, you didn't mention rerolling damage rolls per se, but why not? In case that's interesting, consider the Flames of Phlegethos feat (from Xanathar's again), for tieflings, that among other benefits includes:
When you roll fire damage for a spell you cast, you can reroll any roll of 1 on the fire damage dice, but you must use the new roll, even if it is another 1.
Situational, unless you are the style of wizard who likes to use a lot of fireballs (as many wizards do!).
Now let's try to find spells you can learn earlier in your wizardly career, way before getting 8th and 9th level slots.
Shadow Blade (2nd level, from Xanathar's) creates a magic "sword" that acts as a simple melee weapon with this property:
...when you use the sword to attack a target that is in dim light or darkness, you make the attack roll with advantage.
And that kicks in your Elven Accuracy.
And speaking of 2nd level wizard spells, Enlarge/Reduce, when you use the Enlarge option, you can give yourself advantage on Strength checks and Strength saving throws. Tripped trying to kick down the door? Roll again!
An 8th level elven Divination Wizard could have, besides the Portent feature, both the Elven Accuracy and Lucky Feats, and an owl familiar, and Shadow Blade and Enlarge -- granting re-rolls in several ways.
Altough due to class restrictions they may not be suitable for your wizard:
Another missing feature, at level 1 with Divine Soul Sorcerer you get the ability to add 2d4 to a failed attack or saving throw.
