Travel between the three cities is relatively safe, even at rank 1. Ul'dah is currently the Jeuno equivalent, as everyone goes there to idle, sell there stuff, etc. If you didn't start out in Ul'dah, that's fine, but you'll probably want to make your way there asap.
A few general tips.
1. Sit isn't heal. As long as you don't have your weapon drawn (Press 'F' to toggle this), you will slowly regain HP/MP. If you stand still without your weapon drawn, you will regain your HP/MP faster. Because you weren't moving when you were sitting, you saw your hp/mp regen fast. However, technically, standing still would have achieved the same results.
2. As mentioned above, 'F' key toggles your weapon drawn/put away. You run slower with your weapon drawn, and you don't regen hp/mp. I ran with it out like a noob for awhile during beta.
3. Your intro quest takes you to the "Adventure's Guild" area of your respective town. There are two npcs behind a counter here that offer "leves". These are the fastest way to rank up your fighting/crafting classes at low ranks. You get 8 battle and 8 crafting leves every 36 hours. The timer at the top of the website tells you the next time you get access to 8 more. You also can only hold 8 of both in your journal, so if you grab 8, even if you don't have time to immediately do them, and then come back after the 36-hour timer has refreshed, you can do the 8 currently in your journal and then immediately grab the next 8 from the counter. Handy for if you're busy one night, but don't want to miss out on getting leves.
4. When doing battle leves, you have the option to use 10 Guardian Aspect to get a bonus for a particular leve. This bonus grants you more SP/kill for leve monsters. This is better used on some leves than others. You regen 10 GA per 12 hours. So basically every leve reset, you get 30 more, enough for 3 leves. So generally you pick the best 3 leves you have during any particular reset and use your Guardian Aspect on them. Guardian Aspect caps at 200.
5. Go to Ul'dah. It has the best ~R20ish leveling opportunities, it also has the best R33-50 leveling opportunities. It has the largest market wards for buying/selling items, it's where CKD hangs out, as well as basically everyone else.
6. Now that MP regens the same as HP, I highly suggest everyone at least get some form of sacrifice/cure. I think it's Rank 4 CNJ or THM. There's tons of other good "subjob" abilities to get, so I'm not going to bother listing them here. But self-healing is very useful.
7. All you new players who currently aren't in CKD, make sure you get into CKD. Also, bug "Ket Solais" or "Ridere Tirose" in game to make sure that you have access to the CKD private forums, as well. You'll also get added to the CKD roster.
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