Is it better to pay off a couple of high balance credit cards or several low balance credit cards?

You want to pay off the higher interest ones. It doesn't matter if it is high balance or low balance. You want the highest interest ones gone.

It depends whether you are over the limit on any of them, and then what interest rate they are charging. What I would recommend is to write up a sheet showing all of your cards as follows:

Bank Name -- Amount owed - interest rate - over limit? - min payment.

Sort the list first by anything over the limit and pay those first to stop over limit fees. Then, if there are any with small enough balances that you can pay those in full and stop all interest charges, do those next. When those balances are paid in full, take the payments you were making and use them to pay off other accounts faster.

Finally, if you aren't in overlimit penalty, and cleaned up a low one so you have an interest free card, then hit the ones with the highest interest rate first keeping enough aside to make the minimum payment on the other accounts.

An interesting strategy is to make smaller, more frequent payments online. Say you plan to pay $200 a month. Pay $50 a week instead, and it will drop your average balance faster, and save you interest.

Also, if you have things around that you bought but didn't use, return them and get credits to reduce your cc balances.

Do a websearch on "debt snowball" for other strategies to address this.

Good for you in paying this stuff off!

From a purely mathematical standpoint your best bet is to pay off the highest interest balances first.

However, I believe that if you are trying to get out of debt its a good idea to get rid of your smallest balances first. This has 2 advantages. By eliminating a few small payments, you create a little breathing room in your budget. Plus, it gives you motivation to stick to your plan which can be much more valuable than a little bit of interest saved.