It depends. Your agent should be able to pull other sales in the building so you can base your offer on real data, real sales, and other factors. This is how the bank and the appraiser and going to base their value and this really is the way to determine "fair market value".
I will say, in general, that I've had clients recently who want to offer far less than asking price because they've heard, and they feel, that at this time one should always get a great deal. While I certainly agree with this, it is a great buyers market, you also need to look at see if the property is ALREADY discounted to cover the downward pricing that is current today. I have listings in Fourth Ward for various condos and my sellers have pre-discounted their asking price to account for current value -- again, consider the comparable sales from The Avenue and decide what price makes sense based on those.