Ok after playing a lot of games with the main focus on magic my initial impressions were only reinforced:

the current system is micro intensive while it has little strategic importance which is the worst of all combinations.

Here are my suggestions making it better:

City Buff Spells: 

Current Problem: you have to go to every city enchant it wait till mana is regenerated go to the next buff it and so on.

-Remove individual city buff spells, instead the buffs become global i.e. all your cities are effected once the spell is cast

-Add hints to the city UI,  so i can see which spells are currently in place on that city

-if you want to keep individual city buff spells at least make them castable from anywhere in your territory it just sucks having a big empire and riding along your cities wasting a ton of turn just because you learned a new spell

Buff Spells: 

-Remove the current buff system, instead make buffs like arcane weapons auras, i.e. you cast the spell and all units in your stack will gain the buff.

-give the aura buff either an upkeep, a magic regeneration penalty or it just takes some essence as long as active (for example arcane armor has an essence 'cost' of 1,  if your caster has 10 essence and you activate the aura you only have 9 essence however if you deactivate it you will have 10 again)

==> still strategic importance perhaps even more so, but with next to no micro

Caster UI:

-when i have a caster selected and right click on any tile i want a dropbox which gives me all possible spell that could be cast on this tile, for example i have my sovereign selected and right click on a city i can cast city buffs, but if i right click on an enemy i can cast offensive spells and so on

==> right click -> choose spell -> left click -> done  much easier and intuitive then the current system

-the current UI is an impertinence to the player, especially when there are a lot of spells researched it causes eye cancer to find the right icons.

Champions: 

-i think frogboy already mentioned it, but skill trees or something comparable are a must for champions and the sovereign. nearly every 4x fantasy game has a system akin to this. heroes3/aow2 (with the latest unofficial patch) is years old please don't make elemental worse. just increasing stats is really dull.

The adventure system:

-quests need a separate tab so i can see what quests i have active, where they are and how far i have progressed, basically a quest book is needed.

-researching adventuring should give me more option then just to gain access to more quests, maybe give me better skills in combination to point above.

The UI in general:

-need a complete overhaul, frogboy already mentioned that the empire tree is getting some love if you do this right you should even be able to totally remove the whole section on the bottom of the screen (this is the worst part of the ui currently and imho should be just removed for a much better system)

-if i want to build in my city just let me activate a dropbox by right clicking on the city i can then choose to build building or train units

again: ==> right click ->choose building or unit -> left click -> done

-have the bar of city display what is build and how long it will take

-have the city ui display on the cloth map as well if choose to

-spell research need a better ui, basically it should be easier to recognize each sections, i.e. which spells are learned which available and which are being learned. perhaps give each section a different colored background

and most importantly:

-let the player customize the ui to a huge amount (and mean with out mods)