Skyrim's user interface definitely feels dated. Of course you should have SkyUI already, but there are more things you can do, like add new elements and completely reskin the UI. Reskins can change the feel of the game a lot, so they aren't for everyone.
There are a bunch of QoL elements and fixes we can add to the UI.
Quest Journal Fix for SkyUI (for latest AE only, includes SkyUI SE - Flashing Savegames Fix)
Now we can add and change things about the UI, while keeping it vanilla* (and non-vanilla) style.
moreHUD (disable actor info bars if you use TrueHUD)
QuickLoot EE (AE latest version)
Constructible Object Custom Keyword System (SE version) (check "required by" to find addons)
Main Menu Design Replacer (check mods requiring this file for some menu replacers)
Sovngarde - A Nordic Font (or any other font)
STB Widgets (& Revamp)
Toggle Compass Hotkey and Contextual Crosshair or Ultimate Immersion Toggle.
Convenient Dialogue UI (includes Better MessageBox Controls)
Oblivion Interaction Icons if you want icons instead of text. (Requires patches)
The camera is another significant part of the UI experience. The vanilla camera is janky, especially in third person. Let's fix that.
SmoothCam is a foundational camera mod that we highly recommend, especially if you play in third person. It is incredibly customizable and might be difficult to tweak so there are a lot of presets. Some we recommend are Octavian's Preset (one of the more vanilla-feeling), SynErgy Preset, Soft Preset, Game Cine Preset, Modern Preset, and Raven's Gaze. There are TONS of presets out there, so have a look around.
True Directional Movement we mentioned earlier, but can't recommend it enough.
Alternate Conversation Camera Plus adds a zoom-in effect to dialogue and is heavily customizable. Improved Alternate Conversation Camera is another version of this mod that includes an MCM, but both work perfectly fine.
VioLens lets you customize killmoves.
3rd Person Camera Stagger Remover is recommended if you do combat in third person.
Camera Noise adds a very subtle camera-shake effect. Increases immersion tenfold.
There are a few different reskin options. Please note that many of these will include mods such as Stay At System Page, Wider MCM Menu, and Better Dialogue/MessageBox Controls, so read the mod pages to see what you still need to add on your own.
NORDIC UI is one of the most widely used. It is slightly older and there are few other patches you may need. Get the AE fix for the main menu if you use AE, then install Miscellaneous Patches. Then check mods requiring this file for other patches you may need. We recommend the Nordic...ish TrueHUD preset, QuickLoot EE patch, Oxygen Meter 2 patch, C.O.C.K.S. patch, and markers.
Horizons UI is another standalone option. Make sure to grab the Miscellaneous Patches if needed.
Dear Diary Dark Mode is what you will need for the most reskin options. You can use the mod on its own, however most modern UI reskins will use it as a base, due to its customizability added features. Some reskins we recommend that use DDDM as a base are Untarnished UI, Dragonbreaker UI, Immortal UI, and New Horizons UI.
Dear Diary is the predecessor to DDDM. It supports a few reskins like Wood and Paper.
Dragonborn Reskin is a series of mods (all listed at the bottom of mod page) that reskins other UI mods.
Watch this video to find some different mods and opinions. Remember that UI is very subjective as it changes the feel of the game significantly and has a greater effect than you might think. It's good to play around with.