The best bet for this is if you have a friend in the second city, wherever that is, who can text/email/phone you about offers rather than mail them to you if possible. I used to rent a room from a friend in PA for $1 a year so I could have a "legitimate" non Vegas address for one casino whose offers were better for me with a non local address. I no longer play there, so don't use that now. A friend also has the advantage of having a street address rather than a PO Box.
There are also mailing services you can get that will give you a street address rather than a PO Box, if you are worried about that, assuming you don't have a friend in your non-residential town.
Unless you are a super big player casinos probably won't care which address you use, and many people do have two houses, and others are snowbirds with two addresses. So I think for most folks Jean Scott's advice is overly cautious.
Some casinos use email for many offers (Caesars for example) or post them online for you. If you had an second address you could have mail stored up and only pick it up when you are in that town and want any physical coupons.
When you register for a slot club most will easily accept the fact that you have two homes and want mail sent to address A even though your ID is address B. If not, give your ID and then change your address later ("I am moving and haven't gotten my new drivers license yet"). But really, snowbirds are extremely common in Vegas so different addresses shouldn't cause a fuss.