If you're plans are to stay on the Las Vegas Strip, then I would decide against renting a car. There are many ways to get around and since you're not afraid of walking, you should be fine. Just be sure to have some comfy shoes! Also, keep in mind that certain times of the year it can get hot so you may want to plan your route where you can take pit stops into air-conditioned casinos. I've walked on the strip at night and found it to be no trouble. Just be sure to take any normal precautions like watching your purse, staying in well lit areas, etc.
There's always the
Las Vegas monorail that can take you from the
Sahara down to the
MGM with various stops and on the opposite side you've got the
TI to Mirage Tram or the
Mandalay Bay to Excalibur Tram. If you want to go off the strip may
rent a car for a few days, depending on how long you stay but there are definitely other
transportation options.