Suggestions

In terms of recognizable names, you can see Daniel Radcliffe in The Cripple of Inishmaan or Neil Patrick Harris in Hedwig. Both have tickets available for less than $70. Those are both kind of theater-y shows but you didn't give much to go on. What does your girlfriend like? Do you want a musical or a play?

Perhaps tickets are cheaper pre-sale for out-of-towners, but for us New Yorkers who have the flexibility of "any" time, ongoing discount codes and programs, TKTS, rush seats, lotteries, and access to the box office, etc. purchasing our theater tickets as opportunities present themselves provides better seats at substantially favorable pricing.

Today, shows truly are sold with variable pricing. It can be quite confusing and even more frustrating, but with persistence and a fair amount of money, I get to see most everything - in excellent seats and affordably (well, that's a matter of opinion).

There are a lot of great shows performing now and planned for "June-ish". If you're open to what's available on TKTS or willing to get up early and try for RUSH (how old are you?), your options open up exponentially.

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Elephant Man with Bradley Cooper is not coming in by June this year. Won't be around til next season.

I would try Matilda. You can get seats in the balcony.

neon- yeah I was looking at Matilda, Im just worried it will be a little to childish, no pun intended.

Art- thanks! I think I'll add newsies and Pippin to my list, they seem fun. And I appreciate it....wish I lived closer so I could go to more shows

Yeah, Much Ado will be there but that's a lot like a rush in many ways-you need to get there early. (Or go and sit in the standby line.)

I highly recommend Pippin and Kinky Boots. Given your criteria, I'd put those at the top of the list.