Anyway, I need some advice on what kind of adventure to run and what threats to add in that are appropriate for the player.
Don't worry. A fantastic game can be had by just one player and one DM.
I'm running a game right now, for over a year, with just two players of the exact same class, and we've been having a hoot. Of course, I'm running a slightly different d20 that lends itself better to single or duo play (D&D and Pathfinder are, at their heart, designed for Team problem solving). There have been a few RPGs that I've played that are actually better with one player and one GM (the old James Bond RPG comes to mind--fantastic game for just two people).
But, I understand that you want to continue your current campaign. There is really NO REASON that you shouldn't just move on with one player and, the two of you, have a blast.
Change your thinking a bit. Instead of focusing on an ensemble cast, now you're creating a story that features one hero. Your player is your Drizzt, your Conan, your main dude. Before, you were playing a group thing with a Lord of the Rings style ensemble cast. Now, your story has a single main character. Out is the Mission Impossible style stories. In are the James Bond or Jason Bourne style stories (except in a fantasy setting, of course).
If you're playing published D&D or Pathfinder adventure modules, remember that 99.99% are written with group play in mind, and they include challenges for all sorts of character classes. You've got to keep in mind the abilities of your single hero when creating or converting adventures.
Second, you may be interested in a line of adventures designed for single characters. Those types of adventures are out there--they're just hard to find.
For example, if your one PC is a Barbarian or Ranger class, then check out the 1-On-1 Adventure series by Expeditious Retreat Press. They've got an adventure called The Forbidden Hills that is expressly written for one player and one DM. There are other adventures that focus on other character classes in the 1-On-1 Series, too.
Playing with one player, you've got a few options.
Option #1 - Adjust the Scenario to Fit the Single PC: Design your scenarios (or convert published adventures) so that your PC can handle all the challenges by himself (or have him run, if that needs to happen). If your PC is weak in combat (maybe a Thief class), then be mindful of that. One enemy fighter of lower level will probably be more than enough to face the Thief, one-on-one.
Set up ways for the PC to find NPC allies in the scenario. Or, allow him traps that he can use to take out large swaths of enemies. Always give him plenty of shadows and what not to hide in. You get the idea.
You want the adventure challenging, as always, but consider the character. I'd set up something different for a single fighter than I would a single thief or a single cleric.
Option #2 - Allow the PC to Hire or Convince other NPCs to go with him: In the old days of 1E AD&D, there was always a nifty game concept of hirelings. When I was introduced to AD&D, the very first scenario I played was the famous (or infamous)
Keep on the Borderlands. I rolled up a fighter, and that one character was mine--all mine. I started out in the town of Threshold (from the adventure), and in a tavern, I heard about the Caves being infested with goblins and hobbies.
Needing coin and craving adventure, I decided that I'd take on this infamous Caves of Chaos, the leader of brave adventurers there to clean out the caves, find wealth, and generally beat the hell out of the native humanoids for the peace and goodwill of the people of Threshold.
But, of course, I was a 1st level character (with 7 hit points, iirc) without a party to lead.
In comes the hirelings rule from AD&D. Need more adventurers? Hire them!
This led to several role play encounters at the pub in Threshold. The DM rolled up several characters real quick of different classes (back then, with AD&D, rolling up a character took seconds--you basically needed stats and hit points and equipment...and you were done).
I met with two or three thieves, then selected one. Befriended a Ranger. Hired a mage. Convinced a cleric to join me. And, before I knew it, I was leading a party of five into the Caves for fame and fortune.
This approach means that you don't have to adjust your scenarios as much to fit a particular character class (your main PC). The way I've always played hirelings (and was allowed to play during my first D&D session) is that the player controls the hirelings for the most part, but the DM always has veto power over what the NPC does. This way, the game goes pretty smoothly with the player controling the entire party, but if the player doesn't play the NPCs as true individuals ("This NPC comes running from across the room, diving, in order to take an arrow for my main character!"), the DM can step in and say, "Nope, he wouldn't do that."
I've also had hirelings turn on me. In my early days with D&D, the youngster that I was, I wasn't as much of a roleplayer as I am today. I remember keeping all the good stuff for myself, being greedy for my PC, while my hirelings got the scraps. In my head, the hirelings were greatful to have the opportunity to risk their lives just to be at my side during the dungeon crawl.
Well, my DM didn't see it that way. At one point, the NPC thief tried to stab me in the back! I was being a rotten leader, and I had a mutiny on my hands. I barely got out of that one with my life! And, when I got back to Threshold, it seems word had spread. It wasn't as easy as it was the first time to recruit more people to lick my heals. I couldn't find a thief at all, and the fighter that I convinced to go with me all of a sudden wanted a bigger share part plus money up front!
Ah, those were the good old days. That happened almost 30 years ago, and I still remember the good times.
Anyway, you get the idea. Your one PC doesn't have to be alone. Hire/convince NPC to come along.
If your PC is a cleric, then maybe he can convince some of the Holy Guards to join hm. If your PC is a gutter rat Fighter, then maybe he can ask around the tavern to see which thief might be interested in making a little coin. If your PC is a thief, then maybe he can convince that mage he did a little work for last month to come along on just one adventure....
That angle is wide open to you.
Option #3 - Allow the player to play more than one character: This option is akin to Option #2 except that the DM fully allows the player to run multiple characters. This takes a pretty good playr--someone who enjoys (not just "can") falling into different personalities. Under this option, the DM cannot interfere the way he can if using Option #2 because the extra characters are considered to be all Player Characters.
Back in the AD&D days, I ran the first three adventures of the Dragonlance series this way--just me as DM and one player playing all the roles of the Heroes of the Lance. It worked beautifully. And, we had a ton of fun.
In fact, after the third adventure, I picked up two more players. The one player just divided up some of his lot to where each player had, like, three characters.
I learned that this isn't a bad way to play provided the player respect the fact that each character represents an individual. We would divide the character to where it made the most sense. The same player that played Riverwind would also play the love of his life, Goldmoon. The player playing the mage Raistlin also played his devoted brother, Caramon. I think Tanis and Sturm were played by the same player, and Tasslehoff and Flint were played by the same player....you get the idea.
That worked so well that, for years, when I ran a game, I'd allow each player to roll up two characters. We found that if one got hurt, found himself dead, or, for story reasons, needed to go a different direction, the player still had involvement in the game through his second character.
So, you might want to consider allowing your one player to roll up one or two additional characters, providing he's got the roleplaying chops to play them all as individuals (and not an unrealistic tacitcal fighting group).
Hope all that helps.