I gave a 30-day notice my question is do I have to pay anything during this time

I assume you are talking about a leased property, right? Well you continue to pay rent for the final month plus whatever utilities you always paid. Was this a month to month lease or what, a 30 day notice can not break a longer lease.

Yes, unless you paid first and last month rent when you moved in.

Great point Fr, hadn't thought of that option. Maybe Chef can answer that when he returns.