Boy, where to start...
Well, first thing is most of these changes I'd apply to all spellcasters (if appropriate), not just Wizards:
1. Roll to learn spells. Getting automatic spells of your choice is a huge issue. You can pick one spell to try to learn, if you fail, choose another, etc. until you get one. All other spells must be acquired through research, scrolls, barter, etc.
2. Prune the spell lists. Remove sameyness and overlap. Be more focused with more spells or less focused but fewer spells.
3. Vancian casting. You need to decide what you want to cast and with which spell slots.
4. Increase casting times. Allow spells to be interrupted again.
5. Remove spellcasting foci. Make components matter.
6. Remove at-will cantrips. No more
pew pew pew. Have cantrips RECHARGE! You might have them next round, you might not...
7. Increase DC for spell concentration from 10 to 15. Or better yet, DC based on spell level, like 8 + SL or something.
8. Fix OP/broken spells like
Leomund's Tiny Hut.
Changes I would NOT make or would make to "un-nerf" some of the above:
A. Reducing HP to d4. Damage amounts in 5E are greater than AD&D, so keep the d6--it isn't that much more anyway.
B. Make certain spells rituals, such as
mage armor. It sucks to always have to have it prepared and use a slot on it every day.
C. Get rid of repeated saves (in general). Saves should be a one-and-done thing. Now, you can have failed saves take more time to complete the effects, etc. to allow people a chance to stop them.
D. Alternative to C. If a spell is concentration
and has a repeated save (e.g.
hold person), deny the repeated save as long as concentration is maintained. If the caster drops concentration, THEN you can repeat saves to break the spell.
There is probably more if I think about it... But that's a good start.