Bangkok is a fantastic gateway city to the rest of South-East Asia and I'd recommend spending a few days here after a long-haul flight, before heading off to explore the rest of the region. I like to think of Bangkok as South-East Asia-lite. Buddhism and the Thai way of life are easy to access and it's easy to unwind here despite finding yourself in a bustling city.
If you're in Bangkok for a very short time, I'd suggest staying in a guesthouse within walking distance of the Khao San Road (of the Beach fame) but not on the main drag. I'd also suggest using the Chao Praya river boats to travel between the temples along the River. My favourite is Wat Pho, which is a place of Buddhist learning where one can view the Temple of the Reclining Buddha and also have the best Thai Massage of your life at the Wat Pho School of Thai Massage! Wat Pho is full of lovely quiet corners where you can sit and contemplate life, wonderfully relaxed after your massage.
A great reason to visit Bangkok over a weekend is that the Chatuchak (or J.J) market runs only on Saturdays and Sundays. We always timed our trips to Bangkok over weekends so we could visit this huge market which is great for picking up beautiful Thai curios, clothing and also for kitting yourself out at the start of a South-East Asian trip. Haggling is expected.
After the busy Chatuchak Market, head over to the tranquil Jim Thompson House, a traditional Thai house previously owned by a man rumoured to be a CIA agent, who went missing in the 60's. The house is filled with Thai artifacts and antiques and is a haven from the bustle of Bangkok. The restaurant attached to the museum is quiet and elegant and the food is delicious. Try the Thai Red Curry with Prawns. Heaven on a plate!