You can print off ATIS sheets here for practice.
LiveATC.net does not have ATIS for most airports. There’s usually just ATIS for class B airports, and some of them are very hard to hear. I put a list of links below of the airports with ATIS that are easier to hear.
LAX ATIS (Los Angeles)
MIA ATIS (Miami)
DFW ATIS (Dallas Fort Worth)
LAS ATIS (Las Vegas)