What are some good dates (lunch, dinner, day, etc) in NYC?

http://www.yelp.com/biz/cha-an-new-york in the East Village hits a lot of your stated preferences (Japanese, lots of non-alcoholic beverages, dessert but not crazy heavy, good date atmosphere). My advice to you, from one long time New Yorker to one not-very-familiar with the city, is to avoid anything remotely touristy or symbolic. Your sense of "smell" for these things is not going to be very sophisticated, so if you catch so much as a whiff of "hm, this might be a cliché NYC thing," I would advise that you steer clear. Also, have you considered that since she knows you are unfamiliar with the city, she is expecting the "wooing" to be in the form of... I don't know... gifts? Professions of affection? Not so much with the actually taking her special places? I'm not really familiar with the "wooing" concept but I'm skeptical that she would expect you to swoop in out of nowhere and take her on special dates in a city that is foreign to you.

Don't focus too much on the "NYC" part of this. What kind of dates would you take her on in your hometown? Rent Citibikes and bike around. Bring her flowers. Sit in Central Park on a blanket and drink wine, bring a frisbee and a deck of cards and some books to read (share the Sunday Times if that's your kind of thing). Find some live music - a chill, low-lit jazz bar, perhaps? Cook a meal together (go to a farmer's market, pick out recipes, etc.). Do whatever you'd usually do. Rock climbing? a movie? a concert?

What's your money situation like? That Sunday is the Tony Awards, and they sell http://www.tonyawards.com/en_US/tonynight/tickets.html to the awards themselves. It's usually a fun night (Hugh Jackman is hosting this year), and I think it's impressive.

NYC date things I am a little homesick for: - Long Walks. The High Line is ideal if you want to go to a place for the purposes of walking, but honestly any old place in NYC that is convenient gets the job done. - The Brooklyn Heights Promenade - Loafing around in the grass in Central Park. The first week of June was invented for this purpose. - The Brooklyn Flea or really anywhere food trucks and good people watching congregate. - This is not NYC, but just a good sweet date suggestion in general: I like being taken out for spur of the moment snacky casual desert. This could be anything from a Cronut* to an Italian Ice off a cart in a park. I vastly prefer this to a sit-down "let's Go Out For Dessert" type of situation. - Eataly? - Poorly Kept Secret romantic bars I know about include Angel's Share in the East Village and The Campbell Apartment in Grand Central Station. *I prefer Dough in Clinton Hill or Peter Pan in Greenpoint; there's also Bombolini on the UWS, but YMMV and I think there are tons of artisanal fancy donut places popping up everywhere now.

Free http://www.shakespeareinthepark.org is performing Much Ado About Nothing that week; check the site for details on how to score tickets.

http://noshwalks.com/ http://www.downtownboathouse.org/ (there's a wait) Picnic on the http://www.thehighline.org/

Definitely take a walk on the Brooklyn Bridge. It's free and you get an amazing view of the city. I would say a picnic is a nice idea as well. You could always try getting free tickets to a show (whether it be the Colbert Report, Daily Show, Late Show with David Letterman, Late Night with Seth Meyers, The Tonight Show with Jimmy Fallon, Who Wants to be a Millionaire, etc.). I know most native New Yorkers don't take advantage of how many shows are filmed in Manhattan or they don't think of it. Most of all, I would just say keep up a high spirit and energy and show her how invested you are in this budding relationship and be receptive. It's great that you're being super thoughtful but I generally think that if two people have chemistry and compatibility they will imbue wherever they are with that romantic and tender ambiance they're created with each other. I kid you not some of the most romantic, warm memories I've had (and still are having) have been at places like a McDonald's parking lot and the subway.