@Mjbibliophile Welcome to the community!
We don't have too many members of the community yet from the Mississippi area so we're happy you're here! Don't be surprised if we tag you in the future for your local expertise.
@Jphelps is from Tennessee and gets outside a lot, perhaps they can weigh in with some ideas for your question.
Hey @Mjbibliophile! I was born and raised in Jackson, and still spend a considerable amount of time there. It's so nice seeing another person on here interested in what Mississippi has to offer! Depending on where you're going and what amenities you'd like, Tishomingo State Park is a great option. There's hiking, fishing, mountain biking, and if you can believe it, even bouldering opportunities there. If you're into peak bagging, Tishomingo county is home to Woodall Mountain, the highest point in Mississippi at a whopping 807'! 😂
You can also camp at Sardis Lake, just outside of Oxford. There is a state park (John W Kyle SP) on the western side near the reservoir, or there's also a nice mountain biking trail near Clear Creek area and camping there as well.
If you're looking for a wilderness-type/backpacking setting, I don't know that NE Mississippi has much in that regard, but the Sipsey Wilderness area is just over the state line in Alabama. Sipsey is AL's largest designated wilderness area.