You can find cheap rental cars on Orbitz or Kayak. The prices there are much lower then DL's. The problem with taxis is they are expensive. If you you use them more than once a day, you will find it much more expensive than car rental.
If by tram, you mean the Monorail, forget it. You can reach most Strip destinations easier by walking.
There are buses, but they are painfully slow and crowded. They are a good experience maybe once. You'll tire of it quickly.
Walking is fine if you're in good shape. The big properties in Las Vegas can be right next to each other, but still a healthy walk to each entrance because of their size. I think you'll get tired of walking too unless it's something you do regularly.
If you're not going to drink alcohol, I'd consider renting a good option. There are many good prices for cars, particularly smaller ones. And you can rent from an alternate location than the Airport, which will reduce your cost. Also, you can rent for only a few days and taxi/walk/bus the others.
Lots of options--good luck.