I wanted to check my daily api requests,
/services/data/v37.0/limits/. It consumes an API call.
How do I check one without consuming an API call?
No, you can't call the API from off-platform without consuming API limits.
The API call limit is generally pretty substantial, a minimum of 15,000 + 1,000 per full Salesforce license (other than Developer Editions).
Even if you sampled your limits consumption every 10 seconds, which would be wildly excessive, that's less than 9,000 API calls in a 24-hour period. It's unlikely that a reasonable frequency of API monitoring would cause any measurable impact to your overall limits consumption.