campground near 500 E Cesar Chavez St Austin TX

You're getting a lot of good advice, and I've stayed in most of the parks listed - all good choices. But if your criteria is "closest to 500 East Caesar Chavez" (the Convention Center), Pecan grove is 1.6 miles. An easy drive even in rush hour traffic, and an easy walk along the river if you're able. I've done it several times. Catch the Congress Bridge bat flight some evening while you're there. You're also within walking distance of many restaurants, bars, shops, etc. An eclectic part of downtown Austin.