Where can I find cosmetics?

Outfitters
There are Outfitters in Bree, Thorin’s Hall, Michel Delving, Celondim, Trestlebridge, Othrikar, Stock and Rivendell. Check them all. Items purchased from the outfitter do not bind to character.

Armour Smiths
There are Heavy, Medium and Light Armour Smiths in many towns and regions in Middle Earth. All selling different levels and types of armour for just a few silvers. Go there and try it on with ctrl+left mouseclick! It really looks different on your own character and with another dye colour applied to it. Armour purchased from armour smiths does not bind to character.

Reputation
Special cosmetic items are offered by most factions in Middle-earth (Quartermaster, Reputation barter, Outfitter) and usually require a certain reputation standing to be accessed.

Festivals
Every festival offers several cosmetic items to barter for, and every year a new “themed” outfit becomes available, usually matched with a Steed in the same theme. The Festival Cosmetics bind to account when purchased. There are also “Gift-wrapped” versions available, that can be sold at the Auction House or be gifted to a friend.
The Yule Festival in winter has a questline with specific cosmetic rewards.

Figments of Splendour
These figments can be earned from Festival wrapper quests, Steel-bound lootboxes, Delving chests and Hobbit gifts. They are a currency to purchase cosmetic items from special vendors that rotate through the year. There are 4 vendors that each have a unique inventory of items, and they each appear for about 4-6 months per year at fixed locations, the main one being at the Fountain of Bree in front of Lalia’s Market.

Steel-bound Lootbox
A Black Steel Key (purchased from the Lotro store) is required to open a lootbox. These boxes drop cosmetic items that are in the current rotation of the Figments of Splendour vendors.

Skirmish Camp
You can barter for regular cosmetics and for special “ceremonial” versions of raid armour at the Cosmetics vendor at the skirmish camp. You can also buy all types of older raid armour at the Skirmish Classic vendor. Skirmish cosmetics bind to character if you drag them directly into an Outfit slot, however if you copy the item to your Wardrobe, you can store the original on an alt (or sell it on the auction house). Ceremonial Cosmetics are bound to account.

Quest rewards
Some quest rewards have unique cosmetic properties with a special design that is not otherwise or commonly available. Use the ctrl+left mouseclick option before choosing your quest reward. Stats can be compensated for, but quest rewards are only offered once. Quest rewards are of course already bound to character, so you will have to store them on the character that obtained it.

Token rewards
Raid and Instance Tokens are obtained by running the dungeons of that particular area and are bound to account (or shared wallet), so can be passed to an alt if needed. Some older Raids, and certainly Dungeons, can be done solo by a high level character to obtain the necessary Tokens. However not all Dungeons and Raids can be done solo because of certain game mechanics that require more players.

Loot
There is always the odd chance that you loot something cosmetically valuable, even a grey item like Elven Leather Boots or a Plumed Hat. Burglars have a chance at obtaining “grey” loot by using the burgling skill, which can have a unique cosmetic appearance. Check all armour with ctrl+left mouseclick before selling it.

Auction house
Spend time on the Auction House. Check all armour for appearances, all cloaks and all outfits. Check items with a strange or uncommon name. Check all non-crafted yellow and purple items. Ctrl+left mouseclick is your friend.
Especially uncommon yellow items (helmets, shoulders, cloaks) between level 45 and 75 with the name “of Vigour” or “of Fate” sometimes show up with a unique appearance.
There is a separate section for “Outfits”, but beware because many of these cosmetics can be easily obtained elsewhere. You may check for Gift-wrapped boxes if you’re looking for a specific Festival appearance that you’ve missed.
And while you’re there, check for cheap dyes!

Hobbit presents
The Hobbit boxes that can be opened daily have a chance of dropping three different armour sets: light, medium or heavy armour. These sets are bound to account. The default armour proficiency of the character that you are logged in with when opening the present, determines whether you will receive a light, medium or heavy version. So if you aim for the light version of the shoulders, make sure you are logged in with a lore-master, rune-keeper or minstrel when opening the box. The appearance of these armour sets is currently unique in the game. They used to be PvMP sets, but where removed from the game in 2012. The Hobbit boxes are currently the only way to acquire these appearances.
In addition, Hobbit presents can drop Mithril Coins that can be used to purchase cosmetics at Lalia’s Market.

Lalia’s Market in Bree
Lalia’s Market is the place to go for all kinds of armour pieces presented as cosmetics. Most of these pieces are not unique and can also be acquired through questing or from dungeons and raids, however sometimes Lalia’s is an easier way to obtain these appearances. All cosmetic items are bound to account so you can move them around between your characters. The pieces are on display and when you click on a piece it shows you a preview of your character wearing the piece in the dressing room. You pay for these pieces with Mithril Coins, a currency that you can purchase with Turbine Points, or occasionally find in Hobbit Gift Boxes.

Mannequins
In several locations around Middle-earth you will find four mannequins displaying a full outfit set. Many of these sets have been assembled long ago and feature older armour pieces. The mannequin outfits are changed with every update and rotate over the course of about a year, making these rare and unique sets.
The sets can be purchased with Mithril Coins. The mannequins are now an integral part of Lalia’s Market as well.

Store
Last but not least, there is the Lotro Store. The store has several unique items that you cannot obtain in game, but it also offers some items that are actually quite easy to acquire, so be careful before you decide to make a purchase! Cosmetic store items are bound to account, so you can store all these items on an alt, however to transfer them to an alt you have to make use of regular Shared Storage, as these items cannot be mailed.
There is a “try it on” button in the Lotro store that will allow you to preview the item in the dressing room.