Houston is a big city of separate districts. Downtown has the theaters, arenas and convention center. The Museum District and Montrose are closer to the art museums, parks and restaurants.
Downtown has the Theater District, Discovery Green, George R. Brown Convention Center and major arenas within several blocks. METRORail lines cross the center, but Houston is not a single walkable district. Pick a hotel near the venue or rail station you will actually use.
Southwest of downtown, the Museum District has the Museum of Fine Arts, Houston, the Houston Museum of Natural Science and Hermann Park. The METRORail Red Line connects it with downtown and the Texas Medical Center. Montrose lies farther west, with galleries, the Menil Collection and restaurants. From there you rely more on buses or rides.
The Galleria and Uptown sit west of the central districts around Westheimer Road and Post Oak Boulevard. This is a shopping and business base, not a walk from downtown museums. The Heights, northwest of downtown, has independent shops and restaurants along 19th Street. It feels like a neighborhood, not a convention district.
Houston has two major commercial airports. George Bush Intercontinental is north of downtown and Hobby is southeast; METRO Route 500 links both with downtown. Summers are hot and humid, while winter and early spring are more comfortable for outdoor walks. Allow for heavy rain at any time of year.