For your original question, I'd advise Princes. It's written by the same author as Phandelver, is set in the same area (the SE edge of the Phandelver map overlaps w/ the NW of the Princes map), starts at a more comparable level, and has explicit advice on what to skip if coming from Phandelver. It's almost like it was designed to be a continuation.
I have a fairly low opinion of Tyranny of Dragons, though. I know some folks liked it, but I can't fathom why. I'm not including that as a knock, just full disclosure that I'm very biased.
I have another question, regarding Phandelver--our first adventure. Since it is going to be just the two of us at the start, should we just run two characters (instead of the two each I was thinking of)? -- four seems kind of overwhelming.
As others have, I would strongly caution against having a "PC" while you're acting as DM. I definitely encourage you to run an NPC (or two) while you DM for your nephew. It sounds like a silly distinction, but it's an important one, in my experience. You can't ever really get the "full player experience" with a DMPC; you always know where the secret doors are, where the best treasure is, etc., so you're robbed of the exploration pillar. Also, the role playing aspect gets really weird unless you reduce everything to dice, anyway. Combat isn't horrible, but I wouldn't play D&D for just the combat.
The other problem, especially as a new DM, is that it's very hard to strike the right balance of actually being a PC and wanting to succeed on your own vs. overshadowing any other players. Considering that you're already (by virtue of birth) in a position of respect/authority to your nephew, I wouldn't push it.
The difference between a DMPC and an NPC is where the emphasis for spotlight is. The DMPC is expected to share the spotlight with the other PCs. That's kind of the point. The NPC is supporting cast for the PCs. They can come and go, be a peer or a sidekick, whatever is needed for the story. An NPC party member contributes to the exploration, social, and decision-making process only as much as necessary. If your nephew is about to vaporize himself, the NPC can say, "I have a bad feeling about that." As you get comfortable with NPCs, though, they can sometimes be wrong about things and will have their own goals and motivations.
When I was in high school, I ran a solo game for my best friend, in addition to the regular group game. It was a blast. IIRC, I was running six NPC party members, at one point. It took a while to build up to that because they weren't added until there was a need. It also only worked because the NPCs were there to facilitate the game for the player. In the process, though, we both had tons of fun. I ran two substantive campaigns that way, and he ran a few short-run games, as well.
Perhaps I could let him play fighter, and I would play a wizard, both using the healing surge option? Then I'd just cut the number of monsters in half and/or cut the large monster's hit points in half?
I'd definitely steer him towards a martial character. The Champion Fighter is the quintessential "training wheels" for a new player. Depending on age and/or tactical ability, he might be fine with any Fighter build, though. Personally, I always preferred Ranger or Rogue for solo characters, but that's a mindset thing. I could even see Warlock being workable.
A wizard might be good, but I think a bard might work. It lacks blasting, but has a bit of other arcane stuff, as well as healing. It's generally viewed as a "fifth slot" character, but it also makes a good safety net when you can't cover all the bases well.
Are we going to need a thief for Phandelver? If so, I guess in those cases I could create an NPC thief that is wandering the dungeon and offering his (or her services) at a price.
Thanks!
I don't think there're are locks to pick -- there definitely aren't any that can't be overcome another way. With the background system in 5E, thief skills aren't hard to come by. Our traditional Rogue player was actually a bit irritated by how easy it was for others to dip into "his toys", until he played for a bit and saw how the Rogue really played out.
