Based on successes and failures from many S2000 owners, we can use an offset calculator to figure out what other offsets and tires will work. These are minimum recommended offsets. You can use a higher offset if you want, and you will get additional fender clearance.

For the front:
Offsets lower than +43 are not recommended on the front because a very narrow tire would need to be used to avoid rubbing.
+43 to +47 offset: 205 tires, 6.5" - 7.5" wide wheel
+48 to +52 offset: 215 tires, 7.0" - 8.0" wide wheel
+53 to +57 offset: 225 tires, 7.0" - 8.0" wide wheel
+58 to +62 offset: 235 tires, 7.5" - 8.5" wide wheel
+63 or higher offset: 245 tires, 7.5" - 8.5" wide wheel

For the rear:
Offsets below 40 are not recommended for the rear because a tire narrower than the stock tire would need to be used to avoid rubbing.
+40 to +44 offset: 235 tires, 7.5" - 8.5" wide wheel
+45 to +49 offset: 245 tires, 7.5" - 9.0" wide wheel
+50 to +54 offset: 255 tires, 8.0" - 9.5" wide wheel
+55 to +59 offset: 265 tires, 8.5" - 9.5" wide wheel
+60 to +64 offset: 275 tires, 9.0" - 10.0" wide wheel
+65 or higher offset: 285 tires, 9.0" - 10.0" wide wheel

Note: Verify wheel width by checking the tire manufacturer's specifications . These are guidelines that should work for most wheel and tire combinations.

The offsets above will all set the outside edge of the tire to the same place relative to the outer fender, rounding to the nearest millimeter.
4.1 OEM Fitments
For reference, the OEM MY00-03 (AP1) wheel sizes and offsets are as follows:

Front:
16" x 6.5", +55 offset, 205 tire
Rear:
16" x 7.5", +65 offset, 225 tire

and the OEM MY04+ (AP2) wheels are as follows:

Front:
17" x 7.0", +55 offset, 215 tire
Rear:
17" x 8.5", +65 offset, 245 tire (255 on the S2000 CR)