https://www.propertyfinder.ae/ is a good tool to use for checking property prices in the UAE.
Rents have been reducing and continue to do so. Expect to pay anything from 100K - 150K for a two bedroom apartment in a decent location in Dubai. Popular areas for ex-pats living in flats are the Marina, Downtown or Sheikh Zayed Road (both sides) between the World Trade Center and Dubai Mall.
Hope this helps.