We really liked the Royal Hotel,
http://www.thaifocus.com/hotels/bangkok/royal.htm mainly because of its
proximity to the Grand Palace and the river taxi to all sorts of amazing
places. It is a small, older, Thai hotel and I think you should be able to
get a room for about $US 30. It is also close to Kao San road where all the
backpackers hang out a great place to get inexpensive meals and you will
meet a cross-section of travellers from all over the world. That is also
the place to buy cheap trips around Thailand, but check around with fellow
travellers as some are more scrupulous than others. For a really
fabulous dinner and Thai dancing go across the river on the mahogany barge
belonging to the Oriental Hotel and have dinner at their cooking school.
Expensive by local standards but well worth it. It is nine years since we
were there but at that time we felt very safe wherever we went. We also ate
at many street vendors with no ill effect though I am sure that isn't
everyone's cup of (green) tea!