Van Cleef VC recommended level 18+. It is your first grouped instance and brings lots of water, health and mana pots if you in a group with similarly leveled players. Good Group mixture is a Warrior, Priest, Mage, Hunter, Rogue and so on. It is not careful to draw up to much aggro or it could cost you.
You should be able to do Van Cleef for the green hand without a problem, and also you should venture to Red Ridge and Darkshire. For the Lower 20's, you may stay near lakeshire check out the fields south of it, venture north only with a buddy, there's plenty to do in lakeshire. It happens to be a horde PVP favorite spot to pick of green hand Alliance.
AOE (Area Of Effect) spells is really where a Mage shines. No other class has quite as many AOE spells. You obviously have your Blizzard, Flamestrike, FrostNova. Cone of Cold and Blastwave can be enhanced and added to your arsenal of available AOE spells to choose from.
It's probably a good idea to figure out the most mana efficient way of doing the most damage possible at this time mostly because you will notice that your mana supply will be running out. Gems and pots can supply this of course but, working out the best mana effective routine for AOE's is important.
If you are getting the hang of being a Mage, most of the spells you'll be getting until you hit +60 you now have. You're also gaining world of warcraft gold for your First Mount! The zones known as punishing wow account instances and grueling quests, you'll be in these zones for the better part of the game as you can start in your upper 20's in wetlands and work most of Azeroth from 25-45 but for the time being 30 - 40 is where were at.
In Badlands, there are plenty of quests to get great loot from as well as a great many loot from the instance itself. You can visit many areas of the map, Tanaris, Descolace, Badlands, Southshore, Thousand needles, Swamp of Sorrows, Therefore, wetlands. These are all zones and areas of the map made for mid game. Best advice I can give you is to stick to one zone and get as many of the quests done as possible. Your quest log book can hold 25 quests in it, that's about half a zone worth of quests, as you work them, others will become available the higher you progress in level.