I rode Newcastleton a few years ago and it was pretty good, and I also like Mabie and Drumlanrig Castle, however, from the level you seem to be at, I would suggest Glentress, it's not too far from Newcastleton and the Blue is a fantastic route that really introduces people to the best of mountaining biking without getting too OTT, and you can easily make a mixture of Red and Blue to get the best of both routes. Follow this link and you can become a friend of Glentress and down load the free maps, very helpful.
http://www.7stanesmountainbiking.com/Glentress---Innerleithen
A great route is to park in the Glentress Peel Centre car park, follow the Red/Blue/Black route up to the Buzzard's nest car park, pleasant sngle track with nothing too steep, and a few rocks and balance beams to play on if you like. From the Buzzzards nest follow the Blue route, it rejoins the red after a while, again a fairly easy single track climb, a bit rocky on a few switch backs to make it more fun, unfortunately there's then a wee section of fire road climb, but it's not too long and the views are pretty good near the top. At the top you can stay on the Blue, or take the single track red climb (recommended route), this is quite hard, but not too long and it will eventually get you to the top of Spooky Wood, which is a great Red grade descent, however, all the techincal bits have chicken runs, and most of it is fairly easy, it gets more techinical the quicker you go. After Spooky Wood do the next red section, I think it's called Super G, take this one easy, the start of it is probably the most techincal of this mix and match route, when you cross the first fire road after Super G leave the red and rejoin the Blue (turn right along the fire rad) route all the way back to the car park and cake stop. The Blue descent from here is excellent, Berm-Baby-Berm is probably the best bit of single track suitable for a newish moutain biker I have ever ridden, (I am told possible without braking, but I've not yet managed that) I expect you'll want to do it more than once. The final section of the Blue descent has a mixture of Red and Blue jumps on the way down, you can avoid any you don't like the look of, a couple of te Red ones give a lot of air, but have seen a few painful mistakes. Have fun.
If I was you, I'd probably give Innerleithen a miss, it's a bit more full on, fantastic, but sort of like Glentress' angry big brother.