Booney,
I might be able to provide some advice, I lived in Alice Springs for 7 years. Some of my advice is going to be predicated on the vehicle you are going to be driving, as the most spectacular parts of the NT need serious 4WD. If you are staying on bitumen for the most part there are still a lot of things to see and do, but that's what everyone else is doing.
The big attraction of course is Uluru, formerly Ayers Rock. Biggest monolith on the planet and absolutely beautiful. They have closed the climb, so that's out now but it's still impressive. Nearby is also a rock feature called Kata Juta (sp?), but was called the Olga's when I was there. Really cool hiking through rock formations. There is a resort there but it's fairly touristy. There also King's Canyon a few hours north of the Ayer's resort that is pretty cool to visit. What strikes you the most is the lack of safety regulations - just usually a sign warning you how many people died falling off a cliff taking a selfie.
Alice Springs itself is a cool little town, but from what I understand the crime there has gotten worse in the CBD the past few years. They've cut back on when you can buy take out alcohol and other restrictions. I won't get into the reasons but be aware of that. The casino, horsetrack, and other venues there are still worth seeing. And some of the best true outback restaurants in Australia.
If you go west from Alice, there is Ross River Homestead. Really great working ranch with cabins where you can do whip cracking, horse riding, make damper, and they had a decent pub back in the day. going east is Glen Helen Homestead, which is another great road trip along the Macdonnel Ranges. There are some gorges and waterholes that are accessible on the drive there. The homestead has tourist accommodations and a pub as well. Up the road North from Alice is Barrow Creek, which is just a pub. But a good place to drop in and say hi to the publican and meet fellow travelers. If Les Pilton is still the publican, tell him I said hi.
Going further north up the Stuart Highway (all of these suggestions are on paved roads) you'll get to Tennant Creek, which is pretty avoidable. Then the town of Katherine, and next Darwin itself. In between there are some places to visit such as Kakadu National Park, some waterholes and campgrounds around hot springs. I'd have to look them up because it's been over 20 years since we lived there. Darwin is a cool town, but depending on the time of year miserably humid. And don't even think about the beaches - half the year it's box jellyfish and the other half it's crocs. Or most of the time it's crocs.
Let me know if you'll have 4WD as there are some pretty cool places that you can camp at. Hope this helps!