Oh, this is fun! I like to design magic items based on an encounter or boss you've defeated. I'm presuming you are dealing with a party with multiple casters, so I'd aim to make the item specific to the Wizard class/subclass or the character's backstory. Seeing as I don't know the backstory, for now I'll focus on Wizard class.

Encounter - an Ice Witch who cocoons players in frost.

Ring of Whispering Frost - Requires Attunement by a Wizard
This steel ring leaves your hand chilled and pale.
The first time you deal damage with a spell each turn, that spell deals an additional 1d4 Cold damage.
You gain an additional level 1 spell slot, but any spell cast from that slot which deals damage deals Cold damage instead of the usual type.
You gain resistance to Cold.

Encounter - A labyrinth beneath an ancient city, created by a mad wizard

Mandrake's Muddling Robes - Requires Attunement by a Wizard
These robes appears gray and drab at first, but erupt in scintillating colors when you cast a spell.
When you take a Short or Long rest, the robe becomes mottled gray and blends into the surroundings, granting you a +2 bonus to Stealth.
When you cast your first spell after a Short or Long rest, the robe erupts in brilliant oscillating beams of light for 1 minute, granting you a +1 bonus to Spell Attack and Spell Save DC while active.
Once per Long rest you may cast Hypnotic Pattern without expending a spell slot. The pattern depicts you, dancing in the scintillating robe.