Icoca in Tokyo

I understand Icoca can be used in all trains in the Tokyo region (given that most ic cards were made compatible)

However... Can it be used in convenience stores, restaurants, etc in this area?

No problem just same validity based "Suica" service.
http://www.jreast.co.jp/e/pass/suica.html
http://www.jreast.co.jp/suica/area/shopping/machinaka.html
http://www.jreast.co.jp/suica/area/shopping/index.html

Other area IC cards cannot refund and re-issue only.
Basic functions re-charge and e-money part no different.

If cannot find Suica or similar stickers/signs ask staff with showing ICOCA.

(note) About re-charge(Japanese calling only "charge")
- train stations ticket vending machine (except some small stns out of urban area)
- local bus (not all about 70%)
- convenience stores (not all major brands are all)
So shops.restaurants and more are not accept usual just payment only.

I understand Icoca can be used in all trains in the Tokyo region (given that most ic cards were made compatible)

Actually, there are four exceptions to this rule, but they are minor lines which are not in central Tokyo (the Chiba monorail, the Tama monorail, the two lines of the Kantetsu company, and the Seaside Line in Yokohama). Those lines accept only Suica or Pasmo.

For vending machines, combinis, restaurants, etc., whenever you see a Suica or Pasmo logo, you can use your Icoca instead.

There is one more minor exception: Icoca does not work for the touch-system in non-reserved green cars. You can still use Icoca to pay for the green-car supplement at ticket machines, though. This applies to non-reserved green cars that are available on many suburban train lines in Greater Tokyo, and is not relevant to regular tourists, either.