When the lake is at 684' elevation (3 feet above the conservation pool level,) the Blue Hole is part of Lake Travis and most boats can easily reach the location. Below this level, some portage around obstacles is required. According to the Texas Parks & Wildlife website below "Along a navigable stream, the public may boat, fish, swim, camp, and in general carry on any legal activity. Public use must be confined to the stream bed and, to a limited extent, the banks." The website further states "Under a law dating from 1837, a stream is navigable so far as it retains an average width of 30 feet from its mouth up. The width measured is the distance between the fast (or firmly fixed) land banks." Below the falls in the picture below, Hurst Creek clearly satisfies the "average width of 30 feet" requirement.
The website addresses portage around obstacles "Historically, the law of Texas, both in statute and in common law, has protected public rights relating to navigable streams. Although until recently there appeared to be no Texas statute or case specifically dealing with scouting or portaging, several aspects of Texas law seem to support the proposition that a portage right is a necessary corollary to the fundamental right of navigation. The authorities set out below support the principle that when a person floating a navigable stream encounters an obstruction like a log jam or a dam, or some other potential safety hazard, the navigator has a limited privilege to go onto adjoining private land to scout and if necessary make a safe, reasonable portage. The intrusion on private land should be minimized."
The U.S. Supreme Court has explained that under the federal test of navigability (involving capacity for use in interstate commerce) the presence of a portage does not defeat navigability:
"Navigability, in the sense of the law, is not destroyed because the water course is interrupted by occasional natural obstructions or portages; nor need the navigation be open at all seasons of the year, or at all stages of the water."
Economy Light & Power Co. v. United States, 256 U.S. 113, 122, 41 S.Ct. 409, 412 (1921).
Access to the Blue Hole from Hamilton Greenbelt I is not legal as such access would be across private property!
Lakeway, TX, USA: Parks & Trails