Hmm, my suggestion is for 1 on 1, is get an adventure, then create a character that is 5-8 level better than the adventure.

So a 2nd level adventure, you take a 7th level character in, though a 5th level might do, and as Conanistic or Elric, has the adventurer have a friendly NPC friend with them. Of course some of Howards work had the damsel in distress, but not every time. Nestor  in Halls of the Dead, etc was a fighter; so have a lower level NPC with them, with the example above; the NPC could be 3rd to 5th level depends on how you agree with the suggestion.

I am myself a little short of players and in time have been attempting a solo type play, so creating charts etc, but it for Conan D20, so it would be of no great help at it refers to different creatures, etc and it just by no-way near finished. 

I got a lot to do, I working at Larsha, City of the Dead. I post in next few days in Maps forum below, got a lot of maps, so will add some Encounter charts so you might try a random/solo adventure.

This guy with a pen name of Kabuki Kaiser did a couple Asian-themed supplements, Mad Monks of Kwantoom, and The Flower Liches, that include solo adventures in them.  With a bit of work you could port them (literally, as Kwantoom is a port city) into Hyperborea or the Hyborian Age, especially if you're wanting your character to go to Khitai.

Brock Savage wrote:

Last night the wife asked me to run solo adventures in Hyperborea for her apart from the main campaign so she can try something new..  I agree with Caveman and believe that giving her a companion of some kind would help, nothing too fancy. Something akin to a 0 level NPC.   I'm interested in hearing tips and tricks from people who have tried this before. 

I guess it depends on the level of the scenarios, but low level stuff might allow for 0-level NPCs, they can be very helpful, I know. But a good healer might help as a second character, healing is a potent weapon in this game.

Perhaps a 0-level cleric?