Since walking is a concern for your mother, what about maybe getting an electric scooter for her? They are available for rental in Las Vegas.
And yes for walking between the casinos, Downtown casinos have much less distance between them and aren't as huge as ones on the Strip!
RecVPPlayer
lol. I was reading through these replies intending to post the exact same advice about the scooter rentals when lo and behold, the very last post beat me to it.

You'll see people on rented scooters all over the strip. It might be the perfect option. You wouldn't have to concern yourselves with which hotel has shorter strip access or worry about the distances between neighboring casinos. Stay center strip and go everywhere.
I can't agree with the GN for a first-timer. If your mom has never been, it's the strip all the way, IMHO. DO visit the downtown and take in one of the canopy light shows (The Doors is my favorite), but stay on the strip. Book one of the Cirque shows. Love or Mystere would be my first choices.
You might also want to go to the top of the Stratosphere tower at night for the view. Tip: Skip the elevator fee by going to the bar up there. You'll pay the fee for the drink, but at least you get something besides an elevator ride. The bar has full views all the way around earlier in the evening and once you're up there, you can go to any floor you wish (outside deck, for example.)
The bar and restaurant elevators load separately from the pay-to-ride elevators that go to the observation deck and the thrill rides. Look to the right of the main tower entrance on the second floor.