1) Where can I run in Midtown? Is it so frustrating that I should just stick to the treadmill?
You have to be comfortable running in traffic to get to good running without a cab but, if you are, there are lots of options.
If you're willing to get to the East side and go north around 15 blocks you can, in addition to heading South as another poster suggested, head North. Long run suggestion: East side path north (initially next to the FDR, you'll wonder why you're doing this), footbridge to Randall's Island, Triborough Bridge for freaky exposure, Astoria waterfront, back over the 59th Street Bridge. If you go West I'd also advocate going North - by 80th or 90th the other pedestrians thin out substantially and you can either cut in for a few blocks to Centralk Park or keep going to the Little Red Lighthouse and Inwood. With some planning you can pick your way home through Highbridge Park, St. Nicholas park, Morningside Park (there's a waterfall) and Central Park. 20 miles but you'll have seen more of NYC than 95% of tourists.
2) Any recommendations on a good jazz/music club? I am not interested in the big name clubs that charges $30+ to get in the door. So are there some decent jazz clubs in Manhattan with a cheaper cover and relaxed vibe, or should I just look towards Brooklyn for that kind of scene?
This is New York...sorry! Try Bill's Place in Harlem - as authentic as it gets.
3) What art museums are worth a visit? I am also interested in more niche museums I have seen in New York (Mathematics, Transit, etc.)?
Transit's ok, best if you're travelling with young kids. The Tenement museum is usually great, I highly recommend the Cloisters, the Intrepid is fascinating if you're into military stuff, Morgan Museum and library is architecturally stunning and the Museum of the Moving Image is fun if you're into film (they have some of the originals miniature sets from Blade Runner which is enough for me). All the usual suspects are great too, these are just a little more offbeat.
4) Any guided walking tours worth taking?
5) What should I do in Central Park besides walk around?
Ice skate at the North End, get hit by a cyclist, spend a month's rent on a carriage ride.
6) Is the High Line worth a visit?
It's ok and worth a visit but I agree with every word of this. There are no longer any views to be had unless you count gazing on ostentatious piles of extreme wealth: http://nymag.com/intelligencer...owers.html
7) Is Coogan's worth the visit?
8) Who wants to take me on a tour of the NYC marathon course
I will (as much of it as you can run that is)