Here are Kasich's positions. He does not sound like a moderate to me. I'd say center right. The bolded positions are conservative views.
http://votesmart.org/candidate/political-courage-test/27017/john-kasich/#.VrJcZjYrJTY
Issue Positions
In response to the increasing unwillingness of candidates to answer issue questions, Project Vote Smart has researched Presidential and Congressional candidates' public records to determine candidates' likely responses on certain key issues. These issue positions, from the year 2016, are provided below as a courtesy to voters.
Pro-life Abortion: Do you generally support pro-choice or pro-life legislation?
No Budget: In order to balance the budget, do you support an income tax increase on any tax bracket?
No Crime: Do you support mandatory minimum sentences for non-violent drug offenders?
Unknown Position Economy: Do you support federal spending as a means of promoting economic growth?
Yes Economy: Do you support lowering taxes as a means of promoting economic growth?
No Education: Do you support requiring states to implement education reforms in order to be eligible for competitive federal grants?
Yes Energy: Do you support building the Keystone XL pipeline?
No Energy: Do you support funding for the development of renewable energy (e.g. solar, wind, thermal)?
No Environment: Do you support the federal regulation of greenhouse gas emissions?
No Guns: Do you generally support gun-control legislation?
Yes Health Care: Do you support repealing the 2010 Affordable Care Act ("Obamacare")?
No Immigration: Do you support requiring illegal immigrants to return to their country of origin before they are eligible for citizenship?
No Marriage: Do you support same-sex marriage?
Unknown Position National Security: Do you support targeting suspected terrorists outside of official theaters of conflict?
Unknown Position Social Security: Do you support allowing individuals to divert a portion of their Social Security taxes into personal retirement accounts?