We visited and camped at Great Basin just after the 4th for four days. While it rained on and off and pushed us off the astronomy programs and viewing the clear night sky, the kids (15,7,4 & 2) had a great time camping and doing the Lehman Caves shorties tour. Deer, chipmunks, squirrels, hawks and a little bunny were all part of the local fauna, while wildflowers, pines and aspens met the sage, pinion and junis for the flora.
The camphost, not so friendly, the rangers, phenomenal. Torrential rainstorm coning across the desert will be in the storytelling for years to come.
Overall, a great hidden jewel overlooked with so many of the biggies to the southwest of it. Grab your fuel at the stateline and you won't have any reason to interact with Baker (and you'll be the better for not doing so). Get out and explore!