Try to stay on the river - definitely not on KSR. Is the Ibis Riverside within your budget? Also check agoda.com. Look for a copy of the current National Geographic Traveler and read the article on Old Bangkok.

Definitely book your train ahead. I once failed to do that and wound up overnighting in third. NOT a good idea... If you take the train north to the Lao border you can get a bus from Vientiane to Luang Prabang or fly. I loved Champasak and Wat Phu, but if it is that or LP, go for LP.

When I go I'll stay in the Siam or Pathumwan areas. It's the epicenter of Bkk IMO..