The Banglamphu (บางลำพู) district is located to the east of Ko Rattanakosin, and there are quite a few decent sights round here. It's not well defined where Banglamphu actually starts and finishes, and some sights included here such as Wat Saket and Wat Suthat are sometimes considered to be outside Banglamphu.
About 10 minutes walk north of Sanam Luang (in Ko Rattanakosin), is Khao San road (ถนนข้าวสาร). This is home to a very lively travelers scene, and a mass of budget accommodation is here. Some love it, some hate it but it's worth walking down even if you don't plan to stay here. A extensive market with a huge range of goods, from cheap clothes to Thai handicrafts, many inexpensive restaurants and all the different types of people that come here can make it a interesting experience. Somewhat surprisingly, the nearby backstreets retain a genuinely Thai feeling, much more so than Bangkok's other main tourist accommodation areas, Sukhumvit and Silom. The start of the film The Beach was also set in Khao San road, though filmed in Manila as the real Khao San was judged to be not 'realistic enough'. The guesthouse rooms shown in the film are accurate enough, but if you come expecting to be challenged to drink snake's blood as you walk along the street, you'll end up disappointed.
About 5 minutes from Khao San stands the 24m tall Democracy Monument. (อนุสาวรีย์ประชาธิปไตย). This dominates busy Ratchadamnoen Klang road, and was made to commemorate Thailand's 1932 switch from absolute to constitutional monarchy. Equally noteworthy, but for the wrong reasons, is that it was here that many Thais were killed protesting against a military coup in 1992. The design is of a large copper tray (which weighs 4 tonnes) carrying the constitution, supported by a pedestal. It's a bit of an effort to reach the monument if you want to get close though, as it's in the middle of a traffic circle that always throngs with traffic.
A few minutes walk north west from Khao San is Wat Bowonniwet (วัดบวรนิเวศ). It's not particularly impressive compared to other Bangkok temples, but is notable as the headquarters for the Thammayut monastic sect. This is Thailand's minority sect, the Mahanikai sect is the large majority (headquarted at Wat Mahathat in Ko Rattanakosin). King Mongkut, Rama IV, spent most of his 27 years as a monk here. Subsequent kings have followed this tradition and spent a short time ordained as a monk here, including the present King Rama IX. It also houses Bangkok's second Buddhist university (after Wat Pho).
Further down Ratchadamnoen road is Wat Ratchanada (วัดราชนัดดาราม) and neighboring Loha Prasat (โลหะปราสาท). Wat Ratchanada is not in itself especially worth visiting, but is interesting for the amulet market in the south of the courtyard. There is a large range here, and the ones perceived as most valuable will sell for many thousands of baht. Even if you've no intention of buying, it's worth a look. Nearby Loha Prasat, 'metal castle', is hard to miss. It's an impressive, multi tiered structure with 'resembles, more than anything else, an ornate wedding cake festooned with 37 candle-spires' according to the Moon guidebook.
Cross over a couple of roads from here to reach Wat Saket (วัดดสระเกศ) and the Golden Mount (ภูเขาทอง). Wat Saket itself is pretty unexceptional as far as Bangkok temples go, but lies at the bottom of the artificial hill known as the Golden Mount. This is almost 80 meters high, and was the highest point in Bangkok at one time. It was originally designed by King Rama III to be the greatest chedi (golden spire) in all of Thailand, but it collapsed due to Bangkok's sinking ground. Rama IV merely placed a much smaller chedi on top of the remains, and finishing touches were added by King Rama V. It is possible to climb the 320 steps up to the top of the Golden Mount for impressive panoramic views of Bangkok. A lively festival at Wat Saket in November involves a procession up the Golden Mount.
Wat Suthat (วัดสุทัศน์) and the Giant Swing (เสาชิงช้า)lie on the fringes of Banglamphu, about 5 minutes walk from Wat Ratchanada. The Giant Swing is two high wooden red pillars that were previously the center for an annual ceremony in honor of the Hindu god Shiva. A bench was suspended from the swing, and teams of young men would be swung high to catch a bags of gold or coins with their teeth, which was hung on a nearby 15m high bamboo. This was banned in 1933, due to the high number of injuries and deaths that it resulted in - not really surprising considering how high it is. Wat Suthat is notable for it's huge viharn and bot (both are types of chapels), impressive murals, intricately designed doors, 8 meter tall Buddha image and a large number of statues and pagodas.
To the east of Wat Suthat and the south of Wat Saket, almost in Chinatown, is what has become known as Monks Bowl village (บ้านบาตร). This was originally established by King Rama I as an area where monks black alms bowls, used to collect food, were made. It has shrunk in size since then due to the cost and time of producing these bowls by the traditional method. Nowadays they are being replaced by more modern techniques, but it is still possible to see the bowls being made traditionally. They, and other religious items, are on sale in the streets around here and cost around 500B.
South of Wat Suthat is the little visited but reasonably impressive Wat Ratchabophit (วัดราชบพิธ). It's most striking features are the glass encrusted chedi, and the intricate decoration inside.
Details
Wat Ratchanada, Wat Bowonniwet and Wat Saket are open everyday 06.00am to 6.00pm, and are free. The Golden Mount opens from 7.30am to 5.30pm and there is a 10B charge payable at the top. Wat Suthat is open everyday from 09.00am to 5.00pm, and costs 40B. Wat Ratchabophit costs 10B to enter, and is open everyday 08.00am to 5.00pm
Wat Pho, Wat Phra Kaew, Wat Arun, the National Museum and other Ko Rattanakosin sights are easy to get to from Banglamphu. There is also plenty of budget accommodation options on Khao San road and the surrounding area, as well as a couple of more upmarket choices.
Ordinary buses 2, 15, 39, 44, 47, 59, 68 and 79 all stop on Ratchadamnoen Klang road, as do aircon buses 3, 9, 11, 39 and 44. Tha Phra Athit river express pier is in Banglamphu, about 5 minutes walk north east from Khao San road, and there is a Khlong Saen Saep pier near Wat Ratchanada.