1. Better combat: Now Skyrim was a huge step up from Oblivion in terms of combat but its still got plenty of room for improvement. The main ways I would like to see it improved would be through greater enemy variety, better combat AI (and this goes for NPCs too, random shopkeepers and so on shouldn't be charging vampires and dragons when there are guards and the PC around to handle it) doesn't need to be too fancy but enemies that actually make use of tactics like stealth, supporting each other (say a restoration mage supporting some other enemies), and so on would be fun. It would also be cool to have magic weapons (particularly for important artifacts) that act differently than normal weapons, having say Volendrung have a power attack that slams the ground for a shockwave would be awesome for instance. Making the different weapon types handle differently beyond swinging at slightly different speeds with slightly different reach would be nice, different attack patterns for instance. More options in combat would be good as well, plunging attacks for jumping down on enemies, parry/ripostes (possibly as some sort of timed blocking thing), there are a lot of different ways it could be added to. Improved stealth would also be good (I'd look to Dishonored for examples on how to improve this), though a lot of that falls improving the AI.
2. More/better skills: Again I think Skyrim did a pretty good job here overall, the perks were fun but again there is plenty of room for improvement. Spellcasting was kind of nerfed, and while I personally don't mind the loss of spellcrafting I do think there should be a greater variety of spells, as well as better scaling for spell effects as a lot of schools of magic (destruction in particular) become nearly useless in the late game. Bringing back some removed skills would also be greatly appreciated, an actual unarmed skill would be nice, I would combine acrobatics and athletics to create a skill to add more mobility to combat. I don't really mind mysticism missing, though I would like to see the spells Mark and Recall, and especially levitation be brought back. Finally it would be nice to see more uses/more variable uses for existing skills, lockpicking could use more useful perks, speechcraft has a lot of problems as well, and personally I'd like to see alchemy allow you to say craft firebombs, maybe smoke bombs, things like that.
3. Improved immersion: No NPCs should be unkillable (except maybe kids I suppose) its incredibly obnoxious not to mention immersion breaking to get fed up with (for example) Maven Black-Briar for her making stupid threats and trying to kill her, only to find she's invincible because there is an off chance she might become the Jarl of Riften. New Vegas is an excellent example of the game still being able to function just fine while not making anyone invincible (there are two characters who come back from death, but there is an in universe explanation). I know there is concern of a player being locked out of a quest, but that just means you need to have backup ways through a quest, or depending on the quest just let it be lost. Improved AI could also help with immersion, especially for stealth as enemies should have an alert state they go to rather than deciding that the arrow sticking out of their head was 'just the wind', not necessarily the same hunting for who shot them but certainly keeping an eye out more. Finally better writing would do a lot for this, after all there are a lot of quests and characters in Skyrim that act nonsensically or stupidly.
4. Better quests: More quest variety, longer faction quests, and quests with more options/choices. There are some good examples in Skyrim even such as the Dark Brotherhood quest, which is overall pretty fun with some creative missions, and while its writing isn't that good it does even give you the option to wipe out the faction instead of joining it, which is an awesome choice to have (shame there isn't a similar option with the thieves guild) and while I don't think there needs to be an option to wipe out every faction just having different ways to handle them would be nice.
5. Optional Hardcore mode: Hunger, thirst, sleep, and depending on where in Tamriel its set maybe even a mechanic regarding staying warm like the frostfall mod on Skyrim. Keeping this optional would be ideal as some people would hate it while others would really enjoy it.