I need a mother's advice

So my parents recently moved to a different state. I'm home from college and am visiting for about a month (I'm 21). However, I feel lonely, and would like to go out by myself and not with my mom or dad. They've shown me around but will they be understanding if I want to go by myself somewhere?

I also have been talking to a guy on a dating app who lives a few miles down the road I feel like they wouldn't let me go out to dinner with him or something. I'm not sure why I'm so nervous to ask them. If you were my mother would you let me explore this new town and meet new people by myself? Thanks!