Have you talked on the phone yet?
I would think the chain of events would go:
email, text, talk, lots of talking on phone, an in-person meeting over coffee (no alcohol - dont want to impare our judgement) at a very safe public place, a longer meeting over a meal and activity (date), a lot of good discussions.
I'm afraid that some use on-line dating sites just for hook-ups, they think 'oh this person is using on-line dating because they are desperate and I don't mind taking advantage of that'.
I'd be very clear about your time-line and what you are not comfortable with - if someone is whiny or pushy then forget it, he does not have your best interest at heart. I'd much rather be alone than feel taken advantage of.
No way would I accept an invite to meet him at his hotel bar and never at my home.
Just as a side note: My first fiance was from NM while I was in MO and we actually met in Washington DC when we both worked a summer program there. We were the best at long-distance relationships and everything was perfect. It was just when we were together in the same place that I couldn't stand some things about him. Took me 3 years to figure out it would never work!