This is a random question, but I was curious what the return policy is generally like at electronics stores in Tokyo.

For example, if I purchase a cheap monitor, take it back to my place, unbox it, and realize it's not compatible with my laptop, will I be able to return it for a full refund to my credit card? If so, within how many days usually?

In the United States, e.g. at a store like Staples, you can generally do this without much of a problem as long as it's within 14 days or so.

How is your Japanese?

In the Japan you can return an unused, unopened item within one week of purchase for a refund to your credit card. Be sure to bring your receipt. At the store’s service counter you would want to ask for “henpin” (返品, “return an item”).

OP was that he would open it and try it on his computer. Would that be a rather more complicated return? I have no experience in that on which to base an opinion.

This is a very good topic... returning stuff in Jpn.
It can be hairy. Returning items has traditionally not been a part of Jpnese culture. Until ~10ys ago, I didn't even know that you could return stuff in Jpn. I've returned things in Jpn, but only things that are unused/untouched. I don't know if I'll ever be able to get used to this culture of difficulty returning things. I'm hoping that Costco will rub off on the rest of the retail industry in Jpn and eventually things will change.

If your item is obviously defected, or you haven't opened it or used it, you're usually okay.
But it's never like US where it's no-questions-asked.
The time frame for return varies by store, and it can vary also depending on whether the return reason is defect or otherwise.
Usually anywhere from a week to 30 days.
Some stores will not let you return certain types of merchandise (like food) under any circumstances.
Some stores require that you first call and notify the store and get prior permission before showing up to return.

I've had some bad experiences trying to return items, including electronics, in Japan. Definitely best to ask the store staff before purchasing. Most of the bigger electronics stores like Bic and Yodobashi have English speaking staff now, so you should be able to get a clear answer.

Or take rustykettle's advice and bring your laptop to the store to try with the display model. But, unless you have some really old laptop, I can't imagine why a new monitor would not be compatible with it... most connections are HDMI or digital now, so it should only be a matter of buying the right cable.

Big thanks for all the responses. It sounds like if I were to open and try out the monitor, it would be unlikely that I'd be able to return it. Helpful to know!