When taking lessons, it can be a bit challenging to keep up with everything you are learning as well as finding time to just noodle around on your instrument. However, I believe it’s important to find time to sit with your instrument and just play.
You should take time to learn a song on your own. I’ve spent many years playing, without formal lessons, just learning how to play my favorite songs. Many times, I didn’t learn the entire song and I learned just the cool opening riff. Each thing I learned though made me a little bit better. Whether it was learning part of the song by ear or learning a new scale, each song had their own challenges and rewards.
Also, don’t forget to keep playing what you have already learned. I know it sounds simple, but many times I have students that are just focused on what they are learning from week to week. They never take the time to play any old songs they have learned. A great way to warm up is to warm up with something you already know how to play. Chances are they will sound even better as you become a better player.
Take some time to try and make some noise on your instrument. I’ve spent many hours (and still love to) sitting with my guitar and just noodling about. My advice is for you to find a scale or chord that you’ve been practicing and just mess around with it. I like to put on a drum track and just see what I come up with. Start by playing up and down the scale with the track, or maybe some other exercises and then just play. You’ll be surprised with what you come up with.