Best ways to reach this part of Houston are Metro light rail trains, Metro city buses, and by car.
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. 
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.
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).
Buffalo Soldiers National Museum (BSNM), 1834 Southmore, Houston, TX 77004, ☎ 713.942.8920, . Monday - Friday: 10:00 a.m. until 5:00 p.m. Saturdays from 10:00am to 4:00pm. Closed on Sundays. Located in the Historic 3rd Ward, the BSNM and is dedicated to the brave men and women of color who courageously served in every great American war and military campaign, offering a complete look at African American military history from 1770 to 2000 (the Revolutionary War to the Persian Gulf War) with interactive multimedia exhibits. The BSNM is an active participant in National Veteran projects, such as the Veterans' Registry Program.Admission: $2.00 per person.
Childrens Museum of Houston, 1500 Binz St., ☎ 713-522-1138, . 9am-5pm Mon-Sat, 12-5 Sun. Fun, educational, hands-on museum featuring a whimsical courtyard with a rail caboose and a bayou river, and indoor exhibits with both a cultural and a scientific element. $5, $3 after 3pm.
Contemporary Arts Museum Houston, 5216 Montrose Blvd., ☎ 713-284-8250, . TWFSa, 10-5, Th 10-9, Su 12-5. Non-collecting museum with rotating exhibits focusing on the ever-changing landscape of today's visual arts.
The Health Museum, 1515 Hermann Drive, ☎ 713-521-1515, . Formerly known as the "Museum of Health and Medical Sciences", this museum is affiliated with the Texas Medical Center. Explore human anatomy, the life of a germ, the human genome, and more.$6 adults, $5 kids and seniors.
Hermann Park, ☎ 713-524-5876 (fax: 713-524-5887), . Approximately 455 acres (about half the size of Central Park in New York City). George Hermann gave the parkland to the City of Houston in 1914. It is accessible via the MetroRail. Encompasses the Miller Outdoor Theater, the Houston Zoo, the Houston Museum of Natural Science, and the Hermann Park Golf Course.
Holocaust Museum Houston Phone: 713.942.8000. 5401 Caroline St. Holocaust Museum Houston is dedicated to educating people about the Holocaust, remembering the 6 million Jews and millions of other innocent victims and honoring the survivors' legacy. Using the lessons of the Holocaust and other genocides, the Museum teaches the dangers of hatred, prejudice and apathy to tens of thousands of people worldwide each year.
Houston Museum of Natural Science, One Hermann Circle Drive, ☎ 713-639-4629 (email@example.com), . Permanent venues include the butterfly center, exhibit halls, planetarium, and IMAX theater, others vary by availability.Adult $9, Child $7, other venues vary.
Houston Zoo, 1513 N. MacGregor, ☎ 713-533-6500 (firstname.lastname@example.org), . 9-6. Adult $8.50, Child $4, free on some holidays.
Hermann Park Golf Course, 2155 N. MacGregor, ☎ 713-526-0077, . $31 FR-SU, other times less.
Japanese Garden, Main St & Sunset Blvd, Hermann Park, ☎ 713-284-8300, . 10 - 6, summer. Designed by world-renowned Japanese landscape architect, Ken Nakajima, the garden was built to symbolize the friendship between the United States and Japan, and to recognize Houston's thriving Japanese community.
Miller Outdoor Theater, 100 Concert Drive, in Hermann Park, ☎ 281-373-3386 (fax: 713-942-0863), . vary. Free professional theater offering a wide variety of shows in warmer months (which in Houston, span April through November).Hillside (lawn) seating is always free, some shows have ticket seating under the pavillion, varies by show..
Museum of Fine Arts Houston, 1001 Bissonnet Street, ☎ 713-639-7300, . 10-5 Tu-We, 10-9 Th, 10-7 Fr-Sa, 12:15-7 Su, closed Mo, except holidays.. Adult $7, Senior/Child $3.50, Thursdays free courtesy of Shell Oil.
Texas Medical Center, . A sprawling medical complex which is home to some of the world's best hospitals.
Houston Maritime Museum, 2204 Dorrington, ☎ 713-666-1910, . Great museum in a converted house. Lots of maritime history from the Spanish Conquest onward. Must see for history or sailing buffs.Donation.
rent a paddleboat in Hermann Park's lake
Miller Outdoor Theater, 6000 Hermann Park Dr, ☎ (281) FREE-FUN, . Located in Hermann Park, every event here is free to the public, from Shakespeare to summer performances by the Houston Symphony. Bring a picnic and a blanket and take a spot on the hill. Wine and beer are also allowed, so long as it’s not in glass.
ZaSpa, 5701 Main Street, ☎ 713-639-4566, . A secluded, luxury spa located on the private 2nd floor of Hotel ZaZa Houston offering a variety of spa treatments for both men and women. Facilities include a pool and spa café.
Events & Festivals
Houston Livestock Show & Rodeo - Reliant Stadium and Reliant Park. March, yearly (March 3-22 for the 2009 season). The world's largest rodeo and includes rodeo events, calf scramble, and music concerts. It is known for its big-name music acts as much as it is for the rodeo. The livestock show attracts professional breeders who bring in their world-class livestock to be judged. There is also a carnival on the grounds. 
Some of Houston's most eclectic shopping is in the small businesses of Rice Village, roughly between Kirby and Greenbrier and around Rice Blvd. and University Blvd.
Benjy's, 2424 Dunstan Rd, (713) 522-7602, Modern American dining. This is a favorite of many locals. They have a location on Washington and in Rice Village.
Bombay Brasserie, 2414 University Blvd., ☎ 713-355-2000. Indian cuisine.
Croissant Brioche, 2435 Rice Blvd., ☎ 713-526-9188. French bakery.
El Meson, 2525 University Blvd., ☎ 713-522-9306. Great choice when you're hungry for ropa vieja or any classic Cuban dish.
Patu's, 2420 Rice Blvd., ☎ 713-528-6998. Inexpensive thai cuisine. Small family restaurant. Has a buffet. Currently closed, probably not opening again.
Kelvin Arms, 2424 Dunstan, ☎ 713-528-5002, . Traditional Scottish pub atmosphere. Good variety of draft beers (including Belhaven), though their strong point is their outstanding selection of fine single-malt Scotch whisky.
The Ginger Man, 5607 Morningside, . 2pm-2am. Fun, casual pub atmosphere with an outstanding selection of microbrewed, regional, and import beers. Where else are you likely to find Youngs ales on tap alongside a Belgian kriek? Nothing beats relaxing out in the Ginger Man's courtyard with a chilly beverage on a warm Houston evening.
Two Rows Restaurant and Brewery, 2400 University Blvd., ☎ 713-529-2739, . Casual sports-bar type atmosphere but with decent sandwiches and pizza and a variety of fresh beers brewed on premise. Many of the beers are innocuously light, but their Route 66 Amber is often quite good, they do seasonal beers, plus they have homemade root beer, which is a winner for the non-drinkers.
Holiday Inn - Reliant Park, 8111 Kirby Dr., ☎ (713) 790-1900, . Great location close to Reliant Stadium and Reliant Park. Offers complimentary internet access.
Houston International Hostel, 5302 Crawford Street, ☎ +1 713 523-1009 (email@example.com), . More of a large family house than a hostel, with bedrooms containing bunk beds for travelers. The house is in the downtown museum district so there is a lot to do within walking distance (Thursday is free museum day!) but it's in a residential area, so shops and restaurants are not immediately nearby. The bathrooms are shared and the facilities are clean. Hostel customs are observed at the hostel.$15.
Holiday Inn - Medical Center, 6800 S. Main St, 713-528-7744,. Great location close to the Texas Medical Center, the world-class hospital complex. The hotel provides complimentary transportation across the Center and further into Houston.
Hilton Houston Plaza / Medical Center, 6633 Travis St., 713-313-4000. Location in the midst of the Texas Medical Center. 80% suites. 100% non-smoking.
MainStay Suites Texas Medical Center/Reliant Park, 3134 Old Spanish Trail, 832-201-3131, . Close to Texas Medical Center and offers free wireless high-speed Internet access.
Houston Marriott at the Texas Medical Center, 6580 Fannin St. Adjacent to several hospitals of the Texas Medical Center and connected to Methodist Hospital via the skywalk.
Hotel ZaZa, 5701 Main St., 713-526-1991, . Upscale boutique hotel with an outstanding location next to Hermann Park and the Museum of Fina Arts Houston, with easy Metro access, elegantly appointed rooms, and an atmopshere of pampered luxury.