Yes, it can be a good idea to close unused credit cards. I am going to give some reasons why it can be a good idea to close unused accounts, and then I will talk about why it is NOT necessarily a bad idea.
Why it can be a good idea to close unused accounts
"I'd like to close the cards." That is reason enough.
Simplifying your financial life is a good thing. Fewer accounts let you focus your energy on the accounts that you actually use.
Unused accounts still need to be monitored for fraud.
You mentioned that you have high credit card balances that you are carrying. This may indicate that you have trouble using credit responsibly, and having more credit available to you might be a temptation for you.
If these unused cards have annual fees, keeping them open will cost money.
Unused cards sometimes get closed by the bank due to inactivity. As a result, the advice often given is that, in addition to not closing them, you are supposed to charge something to it every month. This, of course, takes more of your time and energy to worry about, as well as giving you another monthly bill to pay.
Why it is NOT necessarily a bad idea to close unused accounts
Other answers will tell you that it may hurt your credit score for two reasons: it would increase your utilization and lower your average account age. Before we talk about the validity of these two points, we need to discuss the importance of the credit score.
Depending on what your credit score currently is, these actions may have minimal impact on your life. If you are in the mid 700's or higher, your score is excellent, and closing these cards will likely not impact anything for you in a significant way.
If you aren't that high in your score yet, do you have an immediate need for a high score? Are you planning on getting more credit cards, or take out any more loans? I would suggest that, since you have credit card debt, you shouldn't be taking out any new loans until you get that cleaned up. So your score in the mean time is not very important.
Are you currently working on eliminating this credit card debt? If so, your utilization number will improve, even after you close these accounts, when you get those paid off. Utilization has only a temporary effect on your score; when your utilization improves, your score improves immediately.
Your average account age may or may not improve when you close these accounts, depending on how old they are compared to the accounts you are leaving open. However, the impact of this might not be as much as you think.
I realize that this advice is different from other answers, or other things that you may read online. But in my own life, I do a lot of things that are supposedly bad for the credit score: I only have two credit cards, ages 2.5 and 1.5 years. (I closed my other cards when I got these.) My typical monthly utilization is around 25% on these cards, although I pay off the balance in full each month, never paying interest. I have no car loan anymore, and my mortgage is only 4 months old. No other debt. Despite those "terrible" credit practices, my credit score is very high.
Make your payments on time, get out of debt, and your score will be fine. Don't keep unwanted accounts open just because someone told you that you should.