There are lots of good suggestions so far and some great links to more information. Just a little tip, you might want to post this on and take a look at the Beyond Europe forum. That's where the questions and answers about the US and Canada usually end up.
As you go through your planning, keep in mind that it will be an iterative process until you come up with your final itinerary. And that everyone on the trip will have to be flexible in case of situations where y'all have to make last minute changes.
Clarification on the questions below would help you plan and help others to help you.
You said that the people on the trip are you and your family. What does that mean? How many of you are there? What ages?
As others have asked, when are you planning to go? The weather will be a huge factor wherever you go, especially on the road and outside big cities.
You said that you're interested in history, good food and exploring local life. All three of those interests can be found just about anywhere. And they can vary dramatically from one place to another.
For example, exploring Santa Fe and the areas already mentioned near it, you can satisfy all those interests. You can learn a lot, eat great food and see people living in a totally different way from your local area.
You can do the same thing in New Orleans and the areas around it, but the satisfaction will be of a very different flavor, so to speak.
How much does your group know about the history of the US or Canada? Does anyone have places they've learned about, heard of or even seen on TV that they are curious about? Do they have some things they'd particularly like to do?
If so making lists of those places or things to do could be a starting point. You might even get lucky and have more than one person want to go to the same place or do the same thing.
You will tailor the trip to your group's interests, and the more each person participates in the planning, the better it will be.
You can do some Googling, look at some maps and learn how close those trip options are to each other. If they're close, keeping in mind that nothing in the west is close by NY standards, then you could look for other places to go or things to do in the same general area.
Three weeks isn't really much time for exploring the US or Canada, so you'll have to very selective and set your priorities accordingly. For many of us, the planning is at least half the fun. I hope it will be for you, too.