Agree with Raffles, re: the Madinat complex and this is my preferred choice when staying in Dubai, either Al Qasr or Dar al Masyaf.

On my last visit the area around the Shangri-La seemed very dusty although this may have been a one off. For a budget stay or if you are not too bothered about Beach access then the Grand Hyatt can be a good choice. Check for availability on Hyatt.com for stay certificates which work out to $165 a night including tax.

There is a Middle East Forum and a Luxury Hotels forum both of which have lots on Dubai.