Obviously your dates will affect the price but The Westin Grande Sukhumvit and the Grande Centre Point Hotel Terminal 21 appear to fall within your budget, and have the advantage of being on both the BTS and MRT lines.
The Sheraton Grande Sukhumvit (lovely pool area) is a bit more expensive but in the same area.
Admittedly, I've always favoured Sukhumvit over Silom/Satorn, but regardless of which area you choose, it's easy enough to move between them.