You're asking if your "24Hour Fitness" membership will get you into a "Anytime Fitness". As far as I can tell, the two are separate companies and not related. Unless there is a partnership I haven't heard of, I don't see that working.
I believe if you have a key fob issued by your home facility, it will also work in any facility. I'm a member here in Va and I was able to give into a facility in Texas
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