When reading the words "price is no object," most Hounds would probably suggest Per Se. (I've not been.) You haven't told us when you will be coming to NYC, but if it's very soon, getting a reservation there would be highly unlikely. However, no problem coming up with lots of other options though opinions will certainly differ as to which restaurant offers the "best" experience. (See the overrated restaurants thread which garnered hundreds of responses.) That said....
Regulars on this board know that I'm a huge fan of Eleven Madison Park. Chef Daniel Humm is, in my view, a culinary star, and his French-inspired cuisine is truly sensational! Add to that an excellent wine list, service that is both cordial and professional, and a gorgeous space. Each and every time we've been to EMP, we've had a perfect dining experience. Definitely a wonderful place to celebrate a special occasion.
As for an "only in NYC" experience, that's easy. I suggest you take my (in)famous Lower East Side eating "tour." As you walk the streets of this interesting and historic neighborhood, you will have the opportunity to sample foods that are emblematic of the Big Apple. Here's the tour:
LES Food Excursion
For the quintessential NYC deli experiences, no place beats Katz's, on the corner of Houston (Hey, Texas guys, in these here parts, we pronounce that "how-stun"! lol) & Ludlow Sts. You're there specifically for the pastrami sandwich. When you enter, you will be given a ticket. Instead of opting for table service, do what the "natives" do and get on line for counter service. When you reach the counter, put a $1 for each sandwich in the counterman's tip cup – though not mandatory, it is a tradition -- and order pastrami on rye. He'll give you a piece to taste. If you like it (the best pastrami is juicy and has some fat on it), tell him o.k., and he'll make your sandwich, give you some sour pickles, and punch your ticket. Then, continue along the counter for sides – the cole slaw is good -- and drinks. Find seats at a table in the center of the room. (Tables along the wall have menus on them and are reserved for waiter service.) When you’re done, take your ticket to the cashier in front, where it’s cash only. To pay by credit card, go to the counter at the rear where the salamis are sold. Note: For the purposes of this tour, unless you have a gargantuan appetite, it would be best to share one sandwich in order to leave room for more tastings along the way.
When you exit Katz’s, turn left and continue along the same side of Houston St. You will come to Russ & Daughters, famous for all sorts of smoked fish and many other goodies. It's not a restaurant, but they make sandwiches to go.
After leaving the Russes, continue west a couple of blocks until you reach Yonah Schimmel's. Get a tasty potato knish, and make sure to ask them to heat it up.
Now it’s time for the quintessential NY drink – the egg cream. So, reverse yourself and head east on Houston until you come to Avenue A. (Note: Avenue A becomes Essex St. on the south side of Houston.) Turn left on A and head north until you get to the block between 7th St. and St. Mark’s Place. Look for a hole-in-the-wall candy shop, closer to 7th, with an overhead sign jutting into the street that says, “Belgian Fries.” (The place’s official name is Ray’s, but there is no signage to that effect.) One of the women behind the counter will make you a delicious chocolate egg cream.
When you’re finished licking your lips, go back to Houston St. and make a left (east) one block to Norfolk St. Turn right and walk down Norfolk until it ends at Grand St. Two places to look for at the corner of Grand and Norfolk: Kossar's, for freshly baked bialys (another very NY food) and the Donut Plant (self-explanatory).
Next, walking west along Grand St., you will come to Orchard St. Turn right. At 87 Orchard, snack on a pickle from Gus's World Famous Pickles.
Then, continue to 97 Orchard, b/t Broome & Delancey, where you will find the Tenement Museum. The tour will show you what life was like for immigrants to NYC at the beginning of the 20th century. ( http://www.tenement.org
Once you have finished the tour, Il Laboratorio del Gelato, right next door at 95 Orchard, is a must for some of the best gelato anywhere.
If your sweet tooth is still not completely satisfied, the final stop on this tour should do it. Continue ahead (north) on Orchard, crossing Delancey, then one more block to Rivington St. Make a right and you will find Economy Candy at 145 Rivington.
Note: It’s best not to take this tour on a Saturday since some of the spots are closed because of religious observance. Also, Donut Plant is closed on Mondays.
Hope you have a great visit to NYC. Happy Birthday and Bon Appetit!
Has your 60th come and gone? I see your original post was back in November. If you are still planning I ahve got to throwin my recommendation for Daniel. Not only do I think it is the best NYC has to offer but add in the fact you are celebrating something significant and then this really is the place you want.