New Haven
New Haven is now the starting city for all new characters. It's a very friendly place with good infrastructure (you find nearly all types of shops there) and hunting grounds for beginners. Old Haven is still around (in the east) but it is inhabited by undead now. On most shards New Haven is visited by veteran players, so it's easy to get help if you have problems.
Places of Interest
The bank and the area in front of the bank are a good place to meet other players. On the evening it is usually very crowded there. The moongate is located on the peninsula at the south east end of the isle. Be careful when you venture there, because the farm on the way has been overrun by brigands. There are also corpsers and lizardmen near the gate.
The land on the southwest is inhabited by various animals. It is a good place to train taming or to hunt for various resources like hides and logs. There are many mongbats there that are good training for novice players. If you feel stronger, you can hunt the ettins in the wood near the south coast. There are always a handful around and they give good money (about 200 gp each). From time to time they drop nice beginner items.
Quests
Most trainers offer quests for newbies that require that you gain 50% in the skill they train. As long as you have this type of quest, you can go to Old Haven and hunt undead there. You will have an increased skill gain there. Please note that as long as you have these quests, you cannot buy training from a trainer. You have to abandon the quest and then retake it again after the training. You still get the reward at the end, which is mostly a very useful item. For example, for the necromancy quest you get a fully-filled necromancer spellbook.
Another type of quests are the escort quests. They are given by various NPCs in the wilderness and on the streets of New Haven. They usually announce them when you pass by. You just need to escort them to a specific shop inside the town. They give you 500 gp as a reward (just wait a few seconds after the arrival, then the quest resolves). There is a five minute timer on this type of quests, but it's still a good way to make money.