"Fun" is so subjective that it's hard to make suggestions. I love using this site to play with new skill build ideas though.

As a solo PVE casual player, I've got three character builds that I find insanely fun to play right now:

1) Magicka Nightblade with dual daggers - High spell crit from the Magelight passive, I use Mark Target to reduce an enemy's defence, trigger Merciless Resolve to boost my damage, Teleport Strike in, Sap Essence for an AOE that also boosts my damage, then four light or heavy attacks to make Merciless Resolve morph - summoning a spectral bow for colossal single target damage on par with an ult's damage. I can also cast Magelight before summoning the bow to boost the bow's damage even further.

2) Stamina Sorceror with 2h sword - Expert Hunter for the passive weapon crit. Cast Surge to boost weapon damage by 20% and heal me for a huge amount every time I crit, as often as every second. Lightning Form for a defensive boost that also has passive AOE damage (and can proc the heal from Surge), Critical Charge for a quick entry into combat or just for a guaranteed crit (so guaranteed heal), and Reverse Slash morphed for the AOE damage, so as soon as one enemy in a group is below 50% health it's carnage time for the whole lot of them. I have my weapon crit rating at almost 50% with this build, so although defence is fairly low I'm constantly self healing for massive amounts.

3) Stamina Dragonknight with dual swords - Newest build, focused on Fighter's Guild. I sometimes miss the impact of simple light and heavy weapon attacks compared to my modded Skyrim, so wanted to try building a character that can dish out huge damage with simple attacks. It relies on passives to weapon damage, mainly from the Fighter's Guild tree. The Dawnbreaker ult can give a passive +5%. Every FG ability gives +3%, so I have Silver Bolts for a ranged attack and Expert Hunter for the passive boost to weapon crit, which along with the ult is +14% weapon dmg total. Dual swords passive is another +5%. Medium Armour passive is an extra 12%. Igneous Weapons buff with a passive from the same class tree provides another 25%. So that's a total of +56% weapon damage, and there's a passive from dual wield that increases weapon damage by a further 6% of your off hand weapon's damage value. Dual wield skills are Whirlwind for AOE damage, and Flurry morphed to Bloodthirst for a self heal when needed. Haven't got far enough with this character to say whether it works well yet, but it feels fun to play for me, and I'm touring Tamriel to destroy every single Dark Anchor in the game, because screw questing!

The main thing I've learned is that for solo play, ANYTHING is viable. Check out the skill calculator and try making your own special blend of fun