Houston is building a ground-level light rail system, which can be accessed from the Hilton-Américas by walking (about 4 blocks) north along Avenida de las Américas from Dallas Street to Rusk Street to the Convention District Station.
If walking does not suit you, then board Houston Metro's Greenlink buses. These buses travel along two circular routes, Orange and Green, that make stops at various points in Downtown Houston. Both routes have stops near the intersection of Avenida de las Américas and Dallas Street. For a map, click here: https://www.ridemetro.org/MetroPDFs/Schedules/BusSchedules/412-greenlink.pdf
The Greenlink's Orange Route travels a clockwise circuit between the Convention Center and the Theater District. It provides passengers with access to MetroRail's Main Street Square Station and, if you are willing to ride the complete circuit, to its Convention District Station.
The Greenlink's Green Route travels a counter-clockwise circuit through Downtown Houston between the Convention District and the Cullen Center in Southwest Downtoen. It provides access to MetroRail's Convention District Station (an early stop from the hotel) and the Main Street Square Station.
The Main Street Square Station is on the Red Line. On the Red Line, you can travel south to the Museum District, Rice University, Hermann Park, the Houston Zoo, and the Texas Medical Center. Traveling north one stop will take you to MetroRail's Central Station where the Red, Green, and Purple Lines converge.
Convention District Station is on the Green and Purple Lines. Both lines will take you west to the Theater District. Going east, the Purple Line takes you six stops southeast to the University of Houston South/University Oaks stop, letting you off at the south end of the UH Main Campus. (It's a long ride. Trust the Local Arrangements Committee. You will much prefer accessing the UH Main Campus via the buses that the LAC is providing.)
Here is an overall map of the current Houston Metro Light Rail system: http://www.houstontx.gov/abouthouston/lightrail/fullmap-large.pdf .
Unfortunately, neither of the city's airports is yet served by the light rail system.
