fair price

Best thing to do is to look at area comps and see what other similar units have recently sold for. You can do a lot of that sort of research on sites like this one, and Trulia and Property Shark. Educate yourself as much as possible before putting in any offer.

When visiting properties, note the condition--does the place need a major overhaul? If so, you must factor that into your offer price. Remember that often it is hard to determine from sight alone just how much work a place really needs. If it's an estate apartment, for example, there is often need for major electrical work, which is exceedingly expensive. Kitchens and bathrooms are also money-pits.

Generally asking prices are, in this market at least, negotiable. Sometimes highly so. Remember that the asking price rarely has much to do with the value of the apartment--sellers often ask higher than they think they'll get and as such are willing to negotiate down.

If an apartment has been languishing on the market for a long time (again, something you can look up on Streeteasy), you might be successful with a low-ball offer. Following the same line of reasoning, if a property has just come onto the market, it's likely the seller won't budge much on price immediately.

A few other tips--if you visit, say, a one-bedroom and notice evidence of a new baby, this might suggest a very motivated seller (wanting to move to a larger apartment, or to the burbs, for example). If an apartment is owned by an estate, that can also be promising, as the family is likely eager to unload it. People relocating for work are also often highly motivated to sell.

The other factor to note is carrying costs...maintenance per square foot, what you are getting for that, is the apt a land-lease, etc. If you really want to go this alone (no broker), at least have a good attorney lined up who can go over financials and guide you to the right questions.

Good luck!

Actually, sometimes estate sales are the worst. The heirs all have different ideas what money they should get (even though it wasn't even theirs), and the prospective purchaser gets caught in the middle of the often ugly family dynamics.

I know of one apartment (estate sale) that sat on the market for over four years - could have been sold many times over if the heirs hadn't been incredibly greedy.

If they accept your price, you're the high bidder and over-paid. At least thats' the skeptics view...