To see a new house in your dream indicates that you are taking on a new identity and developing new strengths. You are becoming more emotionally mature.
To see new shoes in your dream suggest that you are overconfident in your success. Alternatively, you may be on a life path that is unfamiliar to you.
To dream that you are at a new school means that you are feeling out of place in some situation. Or perhaps there is a new lesson that you need to learn.
In general, dream of new things and new places correspond to what is new in your waking life. It refers to something that is different or unfamiliar.