I want to be able to walk into a building in a city with my laptop and
be able to communicate with another computer elsewhere in the city
using a wireless network. The base station can have an antenna, but
the visibility of an antenna on the laptop would have to be minimal.
The laptop would not have a line of sight with the base computer, and
could be up to 3 miles away, but could be less.

Is this possible? I have investigated various products:
SPEEDLAN 9000, 3Com 802.11b 11Mbps Wireless LAN Building to Building
Bridge, 3Com Outdoor 802.11g 54Mbps Wireless Building to Building
Bridge.

If this is possible, I would like suggestions of products to use to
set up such a system. I note that a line of sight is not an option.

Many thanks.

That is not possible.
While using wifi and laptop without external antena coverage is max
half mile with line of sight and without line of sight only 200 feet
if good conditions.

There are other options - the mobile phone 3G network can also be
used, giving much broader coverage than 802.11 but lower rates (I
think it's only about 2Mbps).  A guy at work has this in the form of a
PCMCIA card from Vodaphone.  I don't know what the pricing is like
though.