While I agree there are some benefits to Ship or Horn vs. Cat, Cat Island is awesome as well and actually offers some things that make it better than any other MS island. For one, Cat Island is a much safer place to be if the weather gets bad because there are numerous places of safe harbor where Horn and Ship offer very little comparatively speaking.... the best being north bayou where you can enter with your boat and take shelter (if really bad, get under one of the houses on the canal). If you happen to be on the south side of the island and need safe harbor, South Bayou is totally protected.
You didn't say if you are simply looking for a family day on the island or looking to fish (or both) but at this point I'll assume a family day where you are looking for places that are easy to anchor and get access to the beach. Productive fishing can be had in the places I will name but if you are looking to get serious with fishing (and not so much a family day), there is a ton more info to learn in order to take full advantage of fishing Cat and my best advice there would be to hire a good charter and let them know you are looking to learn Cat Island.
First, see if this link works...
https://charts.noaa.gov/OnLineViewer/11372.shtml
It's a decent chart to learn about Cat. It is definitely not exact but for the most part, a good learning tool.
I've attached an image of Cat. Two of the best places to get close to the beach are North Point and Smugglers Cove because there is deep water access nearly all the way to the sand. If you are in a typical 24' center console with the motor tilted all the way up, I'm guessing your boat will draw less than 20", maybe as little as 12". either way, in each of these areas where the red arrows are, you will be able to get within feet of the beach by walking the boat in on medium to higher tides. Be careful on big tide range days where the tide is falling... you don't want the boat to become grounded. Just monitor it throughout the day and if needed, walk the boat to slightly deeper water and re-anchor if the tide is falling out.
might be obvious but pick the place to hang out based on the wind and forecasted wind If E, S or SW winds, North point is good. If anything from the north or SE to S, Smugglers is protected. A strong due west wind is the only problem but many people will pull up to the outside beach (east facing shore) in that instance but you have to be careful here if there are residual ground swells from the SE. If leaving from Pass Harbor: its 11.5 miles to North Point, 12.5 miles to Smugglers Cove (going around the west tip a safe distance for deep water) and 17.5 miles to West Ship Island.