There's no substitute for riding lots of bikes. Pay attention to how upright you like to be, how far forward you like the cranks, how wide you want the handlebars. Pay attention to whether the shifter and brake positions work well for you. Pay attention to how stiff you like the frame to feel.
The only specific advice I would give you is, don't think too small. Right now you just want to do a daily routine in the park, but if you get a bike that just barely lets you do that, you might miss out on some of the other joys of biking-- touring, day rides, grocery shopping, whatever might grab your fancy in the future.
You might also prowl around EcoVelo (http://www.ecovelo.info/), an advocacy site for sensible commuting bikes. That site should give you lots of ideas about what, in general, other people value.
i mean a speed bike for daily 1hr routine circling the park on a paved road, within a budget of ~2k.
one caveat - i have to return home on crappy UES roads
But if you're looking for a fixie, my friends tell me that they love their District (also Trek): http://www.trekbikes.com/us/en/bikes/urban/district/district...
Bikes can come in a 'one size fits all', but you'll be hating your bike if you start liking one particular style of biking.
Post a couple more details and I can get you some decent advice!
That said, if you are looking into a serious racing bike, by all means check biker friendly forums or even look into a central park bikers group on meetup.com.