The only station west of the main interchange station at Siam, National Stadium is number W1 on the Silom line. A stone's throw from Siam Square, National Stadium is useful for accessing -- you guessed it -- the National Stadium sports complex along with a handful of hotels and some notable sights along Rama I Road. This is also the closest you can get by sky train to Khao San Road and the rest of Banglamphu, although it's still a four kilometre walk or 60 to 120 baht taxi ride depending on traffic.
Exit 4 to the east of the station takes you to one of this area's chief attractions -- MBK shopping mall -- which is one of the best places in Bangkok to pick up cheap souvenirs, trendy clothes and electronics. MBK is particularly noteworthy for its entire floor of mobile phone vendors who will sell you a phone and SIM card in one convenient stop on the 4th floor. MBK is accessible through two sky-walks; the closer one to the station takes you into Tokyu department store, but the one we prefer thanks to it being easier to find from within the mall is a little further east.
Continue east past exit 3 along the main sky-walk and you'll find another sky-walk offshoot (on the left if walking away from the station) to the Bangkok Art and Culture Centre. Beyond that are the formidable malls and shopping plazas of Siam Square and the Siam Square BTS station itself.
Exit 2 takes you to the south side of Rama I Road, where you'll find the stadiums, tracks, courts, fitness centre and swimming pool of the sprawling National Stadium complex. The Tourism Authority of Thailand's (TAT) headquarters are also just a short walk west from exit 2 directly on Rama I Road just before the largest stadium. You'll want to come here to file a complaint about a Thailand tour company but there isn't much in the way of helpful general info.
Exit 1 takes you straight to the hip budget digs of Lub d Bangkok on the north side of Rama I. Just west of that is Soi Kasemsan 2, which is home to Jim Thompson's House. A Holiday Inn Express and the flashy Siam@Siam Hotel and its rooftop restaurant/bar are just west of that on Rama I.
Continue west on the north side of Rama I and you'll pass a handful of street restaurants before hitting a Tesco Lotus supermarket. Rama I then ends beneath an expressway overpass, but if you continue west on Bamrung Muang Road you'll hit the cheap clothing stalls of Bo Be Market after another kilometre. A half kilometre further and you'll enter an ancient temple supplies neighbourhood that's home to crumbling but historic Sino-Portuguese architecture and Baan Bat monks' bowl village. Just north of that is Wat Saket and the Golden Mount and just west is Wat Suthat and the Giant Swing, although at that point you would be a lot closer to Democracy Monument and Khao San than the BTS station.
To get back in the vicinity of Siam Square from here, you could hop on a khlong boat ferry at the western end of Bamrung Muang.