In the end, buying a place here can be a bit difficult to navigate due to the intricacies of NYC real estate. I highly recommend enlisting an agent in your search early to help you gauge the market, you may want to set-up some trulia alerts as well - if you have not done so already. We do have "buyers" agency in NY, it is not req'd but at times recommended - there are a few threads about buyers agency here on Voices.
In lieu of cash, and being a fast closing - it depends on the seller motivation. If they need to close in 30 days or less, or if you get lucky and find a distressed home seller it will make a huge difference. It is not likely however that you would be able to find out, but you can tell your agent that you can close in 30 days and that may help with getting a price reduction - especially if the home is on the market for more than 6 months.
Finally, with all of the above, you can figure out how low you should go. Placing a % on it is not my idea of good advice. Some homes are priced perfectly so full asking or above asking could be right, while others are overpriced, and 20% off would make sense. I recommend that when you get here, or even before you do - start looking at virtual tours - video, photos, etc and educate yourself as much as possible, so you will know what 800K SHOULD get you and what 650K should get you.
I personally saw about 30 homes over a year ago when I bought my current property, and I still feel like I got a great deal and my home actually appreciated in value - compared to what I paid for it.
Hope this helps!
To sit here and try to forecast prices dropping is akin to being a fortune teller, you have a 50% chance of being right - and wrong. you cannot "time" your purchase, you just do your best to make an educated buying decision that fits with YOUR financial situation. If those things line up - that is when you should buy.
I appreciate that the overall market gets fairly buoyant around now with wall street bonuses being paid. Is there a particular time of year that a cash buyer could be particularly mercenary? My wife is insisting that this is the last house move that she has left in her so I really want to get the best house for the money, even if it means sitting tight in rented accomodation for a few months.
Finally, what constitutes a "low" offer currently? Are we talking about 10% off? 30%?
btw, great service that you and Trulia are providing.