Midtown Manhattan Suggestions?

I am raveling to NYC in a few weeks with my wife and figured this might be a good place to as any to ask for ideas. We are staying in Midtown East/Koreatown near the Empire State Building and my wife has training for a few hours a day near the Lincoln tunnel in Midtown West. So I will have a few hours with nothing to do after that starts.

My wife is a vegetarian and I am decidedly not, so we are looking for places near either with good meat and vegetarian options. Are there any places near those areas that we absolutely need to check out?

Also, any places I should drop by in my few hours of alone time? Preferences will be given to low-key non touristy options.