A really interesting 'Doctor X Tardis' fanfic I've come across is 'Tardis Tales'. In this fanfic, the Tardis has a sort of consciousness that the Doctor tries to fully understand. It delves into the mystery of the Tardis' inner workings and how it has a connection to the Doctor on a deeper level than just being a ship. It's a short but engaging read that will make you look at the Doctor - Tardis relationship in a new light.
Good character development in both the Doctor and the Tardis is key. If a fanfic delves into the Doctor's past experiences with the Tardis and how it has shaped him, and at the same time shows the Tardis evolving in some way, it's bound to be great. For instance, the Tardis could develop new functions based on the Doctor's needs over time. Also, a vivid description of the Tardis' interior and how it feels to be inside it can really make a fanfic stand out.
Well, they might end up in a completely unexpected time or place. Maybe a planet full of strange creatures that they've never encountered before. It could be a really wild adventure.
Often, it involves exploring the unique bond and adventures between the human Tardis and the Doctor. There's a focus on how this unconventional setup changes their dynamic and the challenges they face together.
One possible plot could be that during the regeneration process of the 9th Doctor, something goes awry with the Time Lord's normal regeneration cycle. Maybe there's interference from an outside force, like a powerful alien entity that wants to disrupt the natural order. This interference causes the regeneration to skip a few incarnations and directly jump to the 11th Doctor. The new 11th Doctor then has to deal with the after - effects of this abnormal regeneration. He might have some strange memories or abilities that are a mix of what the 9th Doctor was supposed to pass on and some new, unexpected elements.
They could also meet in a time - locked situation. The 12th Doctor is trying to solve a mystery from his past, and the 13th Doctor stumbles upon the same situation in her present. At first, they don't understand how they are both involved, but as they start to piece things together, they discover that it's all part of a much larger, more sinister plot. Along the way, they might meet some old friends or foes from their respective tenures as the Doctor. And in the end, they work together to outwit the mastermind behind the plot, all while having some really interesting conversations about their experiences as the Doctor.