Veansa is really very sweet, when he's not being a comedian. ;)
Part of where to level will depend on several things. Your class, your gear, whether you have an out of party buffer and what kind of style play you like.
In general however, starting around level 20 Abandoned Camp is good (at level 21 you can get the first of the Black Lion quest series which nets you more adena per kill for turn in items and opens up a later quest). You can also try the area around Dion in Dion Hills. Cruma Swamplands is also a possibility depending on your class and gear.
One thing you can do is take a look at the mob level information at Stratics.
Leveling an SO solo is not easy, I did it often. You have two choices. Up until it is no longer feasible you can windstrike wind weak mobs or you can use disrupt undead.
If you go disrupt undead, just be careful, some mobs (like zombies) are magic resistant. I went the disrupt undead route and leveled in Ruins of Agony/Ruins of Despair, Cruma Marshland (on the Horror Mist Rippers) and then in Execution Grounds.
They changed the trees in EG though to not be undead, so you can't use disrupt on them any longer. So I've also heard that Rakuls in Field of Whispers will work at the later levels but have not tried them.
Everything is pretty much said...but I like to point out that soloing an SO to 40 will let you pay lots of money. You probably have your reasons to do that, but its not advisable....at all.
As an SO with today's current game structure your best bet starting out is to do Raid Bosses with pick up groups in Dion.
You won't spend a lot of money as the healer, and you can lvl rather quickly that way.
I understand you're trying to "solo" but that's a LOT tougher than it needs to be...that said you can do:
20-25 using Windstrike on the orcs outside Dion.
25-30 in EG using heal on yourself, and duals....even +3 107's will do.
30-40 (much tougher) but the Breka Orcs aren't a bad way to go using the same play style.
OR
30-40 doing fettered souls in Death's Pass with disrupt undead.
The problem is that lvling as an SO solo almost requires having two weapons...duals for the 25-30 spat, and a good MATK weapon for fettered souls in Death's Pass (although I found disrupt undead to be a huge drain on mana...so plan on lots of sitting...almost as bad as soloing a SpS in the old days).
Again...for the sake of your sanity, and in the hopes that you'll continue to play you'd be better served doing pick up Raid Boss groups instead of soloing.
Then you can perhaps afford to try Vea's idea on the next go-round ;)
Shouldn't be too hard for an SO to find a party. Raid parties are great, if you can find a good one (random parties often suck though). Or just find any mage to duo and go wherever he goes ;)