I can tell you personally I'm hoping the balance team messes with overall systems less (runes items) beyond just trying to fix game pacing.
Instead id really like to see a focus on 'fixing' problem champs, ones who are too good in pro especially but also maybe the ones too good in low elo.
So like id really love to see a concerted effort to make azir and kalista feel good in solo queue again, maybe minor reworks of champs like garen too.
Wbu
I would really like to not be belittled by riot next year. That's would be great.
Stop introducing more shit designs that are pointless in this fucking game tell riot jag that putting all champions in one champion is not the answer to make a good design
increase laning phase duration decrease jungle presence in early game Massively work on Ashe to make her less reliant on her team
azir and kalista feel good in solo queue again
for that to happen they need to both have counterplay and not be a "no counterplay champ if played by someone with hands" because if azir becomes viable ever again i'm going to snipe Eika to not queue against him everytime
Delete more than half of the things made by CertainlyT, and undo basically everything Jag has done.
But that's impossible because of the large and edgy portion of playerbase who has no idea what makes a god damn fair competitive game and are more concerned about being cool and shit, while playing blatantly broken nonsense that feature-checks the opponent while the latter literally can't do shit. But fulfilling players' clearly unfair demand for power fantasy is more important everyone playing the game amiright?
I'd like to see more skins. TONS OF SKINS.
On a serious note, I'd like to have all champs up to date in terms of animations, in game model, etc. . . MODERNIZING ALL older champs.
I would like less turbines next year, please! [poppy-wink]
Less freaking damage. That is all, really. I would be the happiest summoner in the world again if that happens. The absurd amount of damage is the sole reason I do not really enjoy League right now.
A riot games rework
give teemo 50 more attack range.
Delete 
DZK
Mordekaiser or Pantheon rework!
I would love to see mobility have REAL drawbacks. Or even better, straight out gutted.
An ultimate skin for Katarina. [sg-jinx] An actual ultimate skin not like ggmf.
No more broken mechanics like akali's w that makes her untargeteable by turrets oe Zoe.
A splash art and/or model update for all the champs that need it.
Another event like Bilgewater's event, ideally focusing on Noxus.
I'd love it if Riot stopped selling Ruby chromas with sets only.
Edit: also I think all chat is a liability. Is just to tilt the enemy team. I cannot even mute oñit becaiñuse when I had it muted I didn't understand why was my team inting till some premade told me "they are being flammed in all chat", now I have to have it on to know who I need to report and being able to tell my team "ignore them" or something like that
A sexy Catgirl Waifu champion and a traditional paladin (brusier/enchanter not tank). They can be the same champ if riot wants to, I think that one character from Konosuba is an example of mixing the two.
Some dedicated balancing towards SoloQ.
Bringing down the too strong champions like 
Make 
fairer to play against.
As Azir main I must agree with you. There is almost no counterplay in laning phase. If I see that you can kill me in lane you will just end up watching me farm from far away and poking you slowly with my q. Sometimes I eill that my enemy laner doesn’t have fun at all. But down side of Azir is that he has a lot lower dmg in midgame compered to other midlaners.
I think Azir is a bit underpowered now, but if they buff him just a little he would get out of hand.
He is super fun to play (at least to me) but his design made him hard to balance.
At the time I'm writing this it's late and I could go on for hours about what I want to see. So here's a quick list:
Better game pace
Quicker response from the balance team on gamebreaking issues. Like what they did to funnel, but a bit faster
A goal to achieve after reaching gold
For Riot to keep an overall rank. I'd much more willing to give positional match making a fair shot if I got to keep my overall rank.
Another AP item rework. The one we got flopped bad
More ways for immobile champions to deal with mobility
Meta's that are less defined, I think that's the right term
Hide and Seek as an experimental mode (literally just to make sure everything feels good), before it becomes a featured mode
A better system for featured game modes. The first system overexposed too many, and now they're never around
More reverts/ partial reverts to failed class update champions 
are the big ones
Duskblade removal
A complete revamp of the Sorcery Tree.
Changes to common pro champions to keep them out of the
group
New Champion/VGU podcasts to come back
Skins for less popular champions
Nexus Blitz is a success.
And as an overall goal, I want to be able to spend a whole day playing League and go to bed feeling like I just had an awesome day. It's been a while since I had that, and I might actually cry tears of joy if it happens again. I think that gameplay wise (massive emphasis on the word gameplay) Riot is slowly moving back in the right direction, and for once I'm looking forward to preseason.
Also, have you seen the tower barricades coming in preseason yet? I think that idea has some real potential.
hopefully Meddler and few of the balance team that has been ruining this game for 4 years get replaced
Lower damage all around, especially on ad champs.
I'd love to see them start punishing selfish people who refuse to do their jobs on the team, but I know that's asking for too much, it would make way too much sense.
remove: Stormrazor.
Rework: RAgeblade -> ADC item.
Nerf: ADCs
Consider: sorc shoes remove.
Revert the old soraka nerfs, grievous wounds for 800 gold just makes the game and champion feel useless due to her minor impact being cut in almost half for 800 gold.
I hear they have some sort of role league so if you're good at mid you have a rank, but if you're set as support that you donno wtf to do, well you have a different rank while there.
I can't wait to see my rank in different roles!
