I’d definitely stay down near Khao San, ideally on Phra Arthit Road. Phra Arthit runs along the river, sort of. It’s my faviourite street in Bangkok. Khao San itself is quite good too these days.
One of my preferred old haunts is the Phra Arthit Mansions, at 800 baht a night it’s more expensive than a three star up in Sukhomvit, but way better. There’s loads of great little bars and eatieries along Phra Arthit and further down on Samsen is the Ad Here the 13th, a brilliant little blues bar. It’s tiny, so best to get there fairly early. Pong, the guitarist and owner, is a great guy and a great guitarist. If you’re lucky, you may be met by Georgia, a large predatory lesbian with a divine gift for singing the blues. Her voice gets better the more she drinks.
Here’s another review.
Don’t be surprised by the steady stream of Thai musicians coming in to wai khru (pay respect to a teacher) khun Pong, he’s a legend.
Phra Arthit Mansions is almost directly over the road from the first stop on the airport bus to Khao San. Alternatively it’s around 300 baht by taxi. In fact, taxis are cheap in Bangkok. Get them whenever you get off the skytrain or new MRT thingee.