Is there a small (pocket size), inexpensive (~$100) device that scans
for publically accessable 802.11 networks?

There are two such utilities available for free, depending on the
chipset of your NIC.

NetStumbler:
http://www.netstumbler.com/
A very well designed utility for a variety of platforms, supporting
the following cards: Lucent Technologies WaveLAN/IEEE (Agere ORiNOCO)
Dell TrueMobile 1150 Series (PCMCIA and mini-PCI) Avaya Wireless PC
Card Toshiba Wireless LAN Card (PCMCIA and built-in) Compaq WL110
Cabletron/Enterasys Roamabout Elsa Airlancer MC-11 ARtem ComCard
11Mbps IBM High Rate Wireless LAN PC Card 1stWave 1ST-PC-DSS11IS,
DSS11IG, DSS11ES, DSS11EG

APSniff:
http://www.bretmounet.com/ApSniff/
If you have a PRISIM2 chipset (such as a DLink) you can try APSniff,
also a free utility, but with more bugs and fewer features.

I do not understand what do you mean by a small inexpensive device and
what
type of output you need, and if the device need to be connected to a
computer
etc.
If you are just looking to find out activity in the 2.4GHz ISM band, a
tuned
field strength meter should do. But if you are looking to identify
real networks
you would need a spectrum analyzer(which could be rigged out of a
small oscilloscope with a down converter for the 2.4GHz band, but it
is not going
to be small, if you use cheap 10Mhz oscilloscopes).  But if you are
interested
in the protocol details(including identifying the ESSID etc) you need
a
protocol analyzer and a 2.4GHz promiscous receiver (a low cost one
could be implemented using a laptop and a prism based wlan pcmcia card
along with free
s/w such as airsnort,netstumbler etc.).  But I do not think that it
could be
very small(like a meter with a lcd readout).  It might be possible to
build
one using off the shelf hardware(such as wlan modules(receiver with
ehternet
PHY),a microcontroller and a lcd driver).  You do need to understand
electronics
and the protocols involved.

Unfortunatly, I have not heard of any device like what you want that
is both cheap and small. The only methods I know of to do what you are
looking for (and I'm very well versed in 802.11b networking) is to get
a laptop with a wireless network card and a program such as what
xargon-ga suggested, or get a compaq ipaq, a compact flash wireless
network card, and similar software (which should exist for the ipaq).
Unfortunatly, neither of these options will come close to your price
range, and only the ipaq will meet your size requirements.

Hello Lukensosek,

You may be interested in this product from www.linksys.com

"http://www.linksys.com/splash/wet11_splash.asp"

It retails for more the $100 dollors but not much more.

It is a wireless bridge for old wireless card incompatible equipment.
Turns Ethernet into 2.4 GHz compatible networks. I have one and it has
been very interesting. You need a pc (I used a Mac with virtual PC) to
configure it the first time. It wants the network names and passwords
for the network to join but if you leave the fields blank it
automatically searches for "any" non-encrypted public wireless zones.
IE airport networks that don't require a password to join. It runs on
120 volts so you may want to get a small transformer and 12-volt
battery to haul around in a bag or something. The device itself has 4
LED's to let you know 4 things a) power, b) Dialog c) LAN connection
d) WLan.  WLan lights up when you enter a Wireless Local area Network
and it makes a connection. This device handles connecting without a
computer asking for a network address and all that.  It has a Reverse
RMA antenna connector so adding different antenna has been a struggle
for me. They are not as common so I think I will have to order the
parts online. This is important should you want to make a Yagi or
Pringles can antenna
"http://www.oreillynet.com/cs/weblog/view/wlg/448". I hope to do a
project to increase the devices sensitivity. I also hope to put a
Photosensitive switch over the WLan LED that will make a buzz or
something when I say, bike around the city and wander into a WLan that
is on the street.
You should note on your search that some WLans although public do have
a log in and password. They have some protection and control on their
end. IE you would only really know about a public network should you
be shopping in a bookstore cafe and see a sign promoting the network
anyways. I hope that more Wireless network sites open up like this
one.  "http://www.nycwireless.net/" To track and promote wireless
Internet.

Good luck and I hope it goes well.
Bushido

Kensignton has just what you want:

<http://reviews.cnet.com/4505-3505_7-30468829.html>

it's about $20.