Same sex marriage is not legal in Ohio at the moment though there was a Federal Court case decision recently that may force Ohio to recognise same sex marriages from other states.
The nearest states where same sex marriage is legal are Illinois, Maryland, Washington DC, Delaware, New Jersey and New York. You'll need to research what the rules and requirements are for each state and even some counties within the state.
The good news is if you want ever contemplated moving to the US, your partner is now able to sponsor you for a green card, but you have to be married (by any state or country), civil partnerships are not recognised.