I am looking for a general "ballpark estimate" for the value of a
commercial property in Brooklyn, NY.  However, as this is not a
critical issue at the time, I don't wish to deal with the hassle of
dealing with an appraisal service/realtor.  Is there any online
resource that will give an estimated value
for this property or lot within a reasonable error range?

Try the New York City Dept. of Finance:
http://webapps.nyc.gov:8084/CICS/fin1/find001I

When I worked in the real estate industry, we used to use a "cap rate"
of 8%, here in the Bay Area, to make an estimate.  In order to do
this, you need the annual gross income of the property.  (Annual gross
income X cap rate = estimated FMV).  Obviously, a very simple and not
exact method.

I did some checking and it looks like the cap rate has increased to
something closer to 8.7%.

The other poster gave you the real estate property tax site for NY. 
The value for real estate tax purposes is not the same for
buying/selling property.  However, the value could be close if a sale
just happened and the sales price/value is included in the property
tax assessment.

Here are a few sites that you can use to derive square foot rental
rates and cap rates for your location.

http://www.eloanmasters.com/s_capitalization_rate_defined.htm

http://www.ncreif.org/pdf/2q2002npi.pdf

http://www.reis.com/affiliate_program/affil_syn_metro_select.cfm?CFID=3296737&CFTOKEN=4010695-000c00e0-74fa-1d97-8f68-80da68740000

http://www.realtyrates.com/commentaryg.html