My husband & I are a couple like you. Definitely not into the typical stuff. You've got some great suggestions already (though I didn't like Wicked - too much of a showy "spectacle" for me). Artisanal is a great place for cheese lovers - but one of the loudest restaurants I've ever been in. You literally have to shout to your tablemate to be heard when it's packed. If you go there, best bet is to reserve the cheese cellar table - it's much quieter in there.
Great place for dance or experimental performance is PS 122 on 1st Ave. in the East Village, just a cab ride or subway down 2nd Avenue. This weekend is a premiere of a work combining live performance and projections of Hichcock's film
Rope. General admission seats are $20:
Reid Farrington | Gin & "It" (http://www.ps122.org/performances/gin_and_it.html - broken link)
We go to dance performances a lot more than plays because tix are usually more reasonable - and we love watching dance. If you like dance, there are seats still available this Fri. & Sat. for the NY Theater Ballet performing at Florence Gould Hall (East 59th St. off Madison). The tix are $25:
Signatures 10 | New York Theatre Ballet
In midtown, there's the Baryshnikov Arts Center, and you may still be able to get seats for the legendary experimental theater company The Wooster Group, performing
North Atlantic (a stage play - they present all kinds of performances at BAC). Tix are $45:
BAC / The Wooster Group - North Atlantic (http://www.bacnyc.org/index.php/events/performances/JRT031110-Wooster - broken link)
At City Center (on 56th off 6th Avenue), this weekend you can see a dramatic play called
The Subject was Roses. I love City Center. Tix are $50:
The Pearl Theatre Company : The Subject was Roses at Stage 2
As for a place to eat, if you like Belgian food and beer, and a relaxed atmosphere, we love
the B. Cafe on East 75th St., between 2nd & 3rd. Small place, noisy but festive, and great food.
A more upscale restaurant we enjoy is
the Lenox Room (http://www.lenoxroom.com/lenox.html - broken link) on 3rd Ave. between 73rd and 74th Streets. Excellent food, great service, a little pricey but comfy.
If you feel like venturing into Brooklyn, the Young@Heart gang is singing at St. Ann's Warehouse in DUMBO. If you've seen the documentary about this amazing group of senior citizens singing modern rock, punk, and all kinds of songs, you know how fun & inspiring they are. Easy to get a cab or subway (short walk from train to the theater) there and back. Sunday matinee still has seats open. Tix are about $45:
St. Ann's Warehouse - Young@Heart