At level 1, what capital cities can I go to?

Depending on your starter race, you should be able to reach the nearest capital city for said race rather easy even at level 1. If you stick to the road you'll avoid any mobs, at least most of them, usually you won't find aggressive mobs close to roads in starter areas and around capital cities. If so they are small packs in some random corner.

Portal is one way, having a high-level friend act as "body guard" is another. You can reach most capital trough portals or even boats\zepplins. Keep in mind you can not enter hostile capitals. Well, you can, but you'll be instantly murdered, and you'd need a friend to carry you all the way.

You can NOT go as a level 1 panda, cause once you leave that starting area you can never return, so nobody can get in there to get you out. And places that require prequests to reach are unlikely to be available, such as Ashran and that pandaria place (never remember the name).

So you can go to:

Horde - Orgrimmar, Thunderbluff, Undercity and Silvermoon city

Alliance - Stormwind city, Ironforge city, Darnassus and Exodar

Nuetral - Shattrat and Dalaran

Alternate way of getting between them is having a friend with a "taxi mount" (mount that can take more than 1 person) to ride you where you want, or of course pay someone to do it, if they are willing.