You could put blankets around all the hard objects and pillows or cushions or more blankets on the floor for when he lands. Budgies are usually excellent fliers but he is probably not used to flying with clipped wings. My budgies learned to adjust to either walking or flying a very short distance when they were clipped. Your budgie may learn that also in a little while. In the meantime you can try to make soft encounters and landing pads for him.
Your bird will be fine my parakeet was the same way but he never got hurt and learned not to fly into anything so don't worry.
Keep him away from open doors, mirrors, uncovered windows, and ceiling fans.
I've had a budgie (parakeet) for a few days, and he is extremely tame. He has only ever bitten me a few times such as when I first tried to put him in his cage. He can even do step up sometimes and likes to have his tummy gently rubbed by my finger, which I think is amazing since I just got him at petsmart. The only thing that scares me is him flying. His wings are clipped, but he can still fly up to about ten feet high, and then he usually runs into something and drops like a rock. I'm so afraid of him hurting himself whenever he falls, but he loves to fly around and explore. I just had him flying in the bathroom and now he is sitting in his cage happily grinding his beak, as he always does after he flies. Is there anything I can do to help him from hurting himself when he is out of his cage?
