Best ways to reach this part of Houston are Metro light rail trains, Metro city buses, and by car.
Train
Houston's Metro light rail system is an easy, comfortable way to get to the Medical Center, Rice University, and Museum District. Trains run down the center of Main Street beginning as early as 4:30am and running as late as 2:15am. Schedules and prices are on the Houston Metro web site. (http://www.ridemetro.org/)
Car
Houston is a sprawling city in which everyone drives everywhere. The Medical Center/Rice/Museum District area lies in between the Southwest Freeway U.S. 59 and the South Freeway TX 288.
From U.S. 59 southbound, exit Fannin, then head left
From U.S. 59 northbound, exit Greenbrier, then head right
From TX 288 either direction, exit McGregor
From I-610, exit Fannin and either head north, or use the Park and Ride lot and ride Metro
Street parking is available in much of this area, and there are public parking lots at the major museums, in Hermann Park, and around the Medical Center the latter are most expensive.
By bus
Several Houston Metrobus routes run through this part of the city. Use bus lines 1, 8, 34, 65, 87, 292, and 298. There is also a local trolley service for the Medical Center. Bus lines for this area connect to the Metro light rail train line at the TMC Transit Center at Fannin and Pressler. Bus stop locations and schedules are on the Houston Metro web site.