What type of attire is acceptable for adults just to run around NYC? Should jeans be avoided? We'll be doing all the typical tourist sites and will dress up for the theater but should we leave all the jeans at home?

Only if you don't want to look like you could be a New Yorker.

If you are touring, where your most comfortable shoes so you can enjoy yourself. You will see people in everything - jeans, slacks, sweatpants, you name it - it's a city - sneakers, walking shoes, stiletto heels, fashion shoes and boots. Wear what you wear normally, your style, and are comfortable in.

You will see people in jeans in the theaters, you will see them in everything from jeans to slacks to dresses - coming direct from touring, work, and those who still dress for a night at the theater.
You will probably feel most comfortable NOT wearing jeans, but nice slacks and a top will do or get as dressy as you like.

I meant you will probably feel more comfortable NOT wearing jeans in the theater, - I wear jeans all the time in the city during the day.

Over 8 million people live in NYC, and countless more are visiting or working there every day. Any and every kind of attire can be seen, and jeans are as common in Manhattan as they are anywhere else.

Unfortunately, (IMO), probably about half of the theater goers these days wear jeans & sweatshirts.

If I'm going out to dinner or to the theater I'll dress nicely, otherwise I'll often wear jeans and have never thought twice about it. Wear what is comfortable. You will neither be over dressed nor underdressed in any typical tourist site.

In other words, wear what you want. Everyone else does.
I do recommend you leave open toed sandals at home (to protect your toesies) and if you want to blend in, wear dark clothes (they stay cleaner.)

what escargot said.

Just try to leave the white sneakers at home!

Wow thanks for all the prompt responses. I'll pack a couple of pairs of jeans among the black pants. I never wear black sneakers and have good black and brown Clark walking shoes.