At times the question of training alone and what should, or can, be done without a training partner comes up. Its difficult to know what to train in as you don't want to do this incorrectly and develop bad habits. I would normally say you need to get your first grading before commencing solo training so you at least have a grasp of the basics.
The first thing to focus on are kamae, being able to move between different kamae, always in balance with the right weight distribution and spinal alignment, Kamae are moving not static so working on transitions help with this and discourages static fighting poses. With kamae practice both armed and unarmed ones to get used to handling various weapons with different characteristics. This reduces the locking up and weapon centred movements that happen when first using a weapon.
After working through kamae move on to kaiten, taihenjutsu (rolling) a skill that can be easily overlooked. A well developed ability to absorb impacts with the ground by skilful application of taihenjutsu (the art of changing the body) can be indispensable in a variety of circumstances. It also improves taijutsu with more adaptable skill. As with kamae practice rolling with weapons as well as without. Again this will improve overall handling of weapons as you progress. Along with rolling also look at skills for shoten (ninja parkour) such as leaping, running up surfaces and climbing.
Then there are certain kata that you can train alone. The five from San shin no kata (Chi, Sui, Ka, Fu, and Ku) are ideal for lone training and develop good alignment for striking, kicking and weapons techniques. As well as striking surfaces to develop skills not only in actually hitting things but learning distance needed to strike with your body weight and to move correctly around a target.
This will hopefully will give you some direction in solitary training and help improve your taijutsu and ability to develop in the art.