Measurement devices would be lovely here. Measurement devices would always be lovely.
On the other hand, we have some data, even if we don't have much in the way of measurement. And from that data, I have a hypothesis.
Places with very low penetration of other races have very low racism. Europe in the '80s was like this. No racism, and no (appreciable quantities of) other races.
Places where there is very low unemployment have comparatively low racism. Houston is like this.
Places where the races are not competitive with one another, or are required to work together in order to solve problems (Koreans(?) own many of the laundromats in California, few people care).
Aretae's 1-stop hypothesis shop says:
Race relations are bad when there is substantial inter-racial competition for positions AND positions are relatively scarce....OR when there is substantial inter-group money-transfer.
Prediction...IT workers have more issues with Indians than with Blacks, because there's no black competition in the IT space.
Prediction...self-employed people (minus construction contractors) are less racially motivated than others, as they are not usually competing against minorities.
Prediction...the better the (city or nation) economy, the smaller the racial issues.
Prediction...California smaller town, middle-class, upper-middle IQ (110) whites are more likely to be anti-asian than anti-black. Asians take college slots from the middle class kids. Blacks don't
Prediction...Affirmative action should be especially reviled by the folks it impacts most...which are blue collar workers. It combines both transfer and competition.
Prediction...Affirmative action should be especially favored in areas where there is little threat of a minority taking "your" position. Academia tops this list, with tenure rules, and very low minority penetration.
Prediction...High welfare mixed race cities will have a lot more racial tension than low-race mixed race cities. Correlary: European welfare states (with poor job creation, and which are developing large arabic islamic minorities who are both massively underemployed and largely on some public assistance) will encounter anti-arab racial tensions within 20 years that make US racial tensions look tame.
Prediction...cutting tax (especially business tax) rates and eliminating minimum wage laws are the top effectiveness activities for improving racial harmony.