Ive heard about justice system, which is a nice thing to do as solo player and also gives good gold.
What else?
Maybe farm tons of CP to be OP and solo adventure zones? (Possible?)
In oblivion and skyrim i spent a lot of time exploring everything, buying all houses and stealing lots of cities... I want to k ow what this game has to offer to a solo player.
1. Achievements
There are some for dolmen, Skyshards, fishing; ...
2. Farming
Well, you can farm quite a lot of stuff to get richlike
gold, nirncrux, set pieces, perfect rogen, crafting resources; flowers, etc.
3. Dailies
Well, Gold Key Dailies are group content which you can do with a few random people; and crafting dailies are useful too.
4. Solo-PvP
A good way to improve your skills. Well, I am more of a PvE-Player, so you would be asking the wrong person.
5. Soloing group content
Well, that is the fun part for solo players.
You can start with doing dolmen and world bosses solo, as well as the mob groups in craglorn and Craglorns dungeons. Careful, the bosses in those dungeons are pretty heavy hitters.
If you can do that without breaking a sweat (except for the fear mage groups in upper craglorn, those are evil), You may want to step it up and try soloing NonVet-Dungeons. I feel like Non-Vet Banished Cells is a good and hard measurement for your skills that can be done with any class.
If that becomes boring, try Soloing Normal DSA. Some Stam-NB already did that.
Of course, it's not like there are reliable builds for soloing that stuff, so you will probably have to make one of your own.