can you use the internet for the n800 anywhere??
Im thinking about buying one can u use the web without problems without a mobile phone?? I live in NYC

You can use the internet anywhere a wifi hotspot can be found... And as far as I know, NYC has more than almost anywhere else.

so i wouldn't be able to use it at any random apartment building

There are two forms of built-in connectivity in the N800:

1) Wifi
2) Bluetooth DUN

If you don't have a mobile phone, you're limited to where you can use wifi.

There's a third possibility involving some hacking:

3) Bluetooth PAN

There's a fourth possibility once the N800's USB host support gets more mature:

4) USB Ethernet adapters

There are devices which take a wired Ethernet or telephone cable and present wifi or Bluetooth PAN.

I'm in Manhattan. Unsecured wi-fi hotspots are increasingly scarce; I think TW Roadrunner leans on customers to WEP-ify.
Big problem is that you'll always see so many networks to try to connect to, but almost all will fail. Generally, first try those named linksys, followed by Belkin and Netgear.
People in Philadelphia can get Earthlink wifi anywhere in town for free until Jan 1. That's a deal one can only get if one signs up using the N800.

I go to school in Manhattan/Brooklyn, and I'm from Miami where I am currently. I wouldn't say you can use the internet *anywhere* with just wifi. If you have a good phone in NYC, you can probably rock 3g connection just about anywhere you get signal, or atleast edge. While in my opinion it isn't exactly hard to find wifi in either Manhattan or Miami (I've wandered around both extensively with my laptop) you might have to take a little detour or two to hunt it down from time to time, but there has never been a time when I needed to get online that I couldnt find a hotspot to suit my needs in a reasonable amount of time. To my knowledge all Manhattan parks rock wifi, I know for a fact Union Square does, as I've sat there and got walked all over by squirels while on my laptop eating the wifi before.

Using wifi anywhere is a broad statement. Any major city has spots you can drive/walk to but just around your home, you better get a wireless router or find someone you can connect to.

Best bet is a phone but I live on the edge of 3G so I am mostly edge. When the phone decides to go to 3G to edge or vice versa, I temporary loose a connection. In real rural areas, you won't even get edge like some of my motorcycle routes in the mountains/hills.

I use the N800 in New York City. I successfully log onto many open sites including the Downtownalliance parkwifi queens library nypublic library and many of the open cafe site. i never pay for the Tmobile fee sites like Starbucks or Macdonalds. In lower and midtown manhattan I found about 135 open free sites inhotel lobbies, restaurants, coffee lounges, bars, parks etc.

You can also log on to a free ISP via bluetooth to your cell phone but the down loads are 9600bps slow (I only use this for text email down loads)

can i just buy like a pocket sized wireless router and walk around anywhere I want
would that work??

No because you have to plug in somewhere.