If I have access to a base but no car, can I just walk onto the base?

Yes. You can walk onto post. You can also ride a bike on post.

While this should go unsaid...but....if you do decide to walk up to the gate, make sure you have your CAC on you.

You certainly can on most bases walk straight up to the gate. Usually your CAC card will suffice as proper identification, but it's not a bad idea to have some other form of photo ID on you just to be on the safe side in case the guards ask for two forms. I know here at JBLM it's on a random check basis that they ask for it. Also, if you plan on going through the gate with a backpack or something like that, be prepared to have it searched by the guards. They frown on people walking up with baggage... for obvious reasons. Hope this helps you out a little better.