No matter where you are staying in Palm Springs, if it is downtown or somewhere close to that, it is great for walking.  The best thing to do is pick up a Palm Springs Officical Vistors Guide.  It is perfect for first time visitors or for anyone just to know and become aware of  what is new, fun and interesting to do.  Part of the charm of visiting Palm Springs is being able to get out and walk to breakfast or dinner.

If you do have a vehicle, you will be happy and pleased to know that most hotels offer ample free parking, although you should pack or purchase a car sun shade to help prevent your vehicle from getting too hot if you leave it in the summer sun for an extended period of time.  

A vehicle will allow you and your traveling companiions to visit some of the surrounding areas such as Joshua Tree Nat'l Park, the Outlet Mall in Cabazon, the Palm Springs Aerial tram, hiking trails, and many more of the places that are often considered "must see" destinations in the Palm Springs area.

Be aware that summer temperatures in the low desert can be fiercely hot as it's nearly always over 100º every day, and temps often soar up to 120º. The sun temperatures are much hotter than the shade temps.  Always carry water with you, as well as a lightweight hat. Be sure your vehicle's air conditioning is in good working order.